This is a multi-part message in MIME format. ---------------0310280251113 Content-Type: text/plain; name="03-476.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-476.keywords" absence of quantum channel, homogeneous potentials ---------------0310280251113 Content-Type: application/postscript; name="HS_271003.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="HS_271003.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: HS_271003.dvi %%Pages: 39 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR10 CMCSC10 CMMI10 CMBX10 CMMI7 CMSY10 CMSY7 %%+ CMR7 CMMI5 CMSY5 CMR5 CMR12 CMMI12 CMSY8 CMMI8 CMR9 CMR8 CMEX10 CMR6 %%+ CMTI12 CMMI6 MSAM10 CMBX8 CMSY6 CMTI10 CMTT10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips HS_271003.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.10.27:1107 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 64 /at put dup 97 /a put dup 98 /b put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 51 /three put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 79 /O put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFB7605D7BA557CC35D6 49F6EB651B83771034BA0C39DB8D426A24543EF4529E2D939125B5157482688E 9045C2242F4AFA4C489D975C029177CD6497EACD181FF151A45F521A4C4043C2 1F3E76EF5B3291A941583E27DFC68B9211105827590393ABFB8AA4D1623D1761 6AC0DF1D3154B0277BE821712BE7B33385E7A4105E8F3370F981B8FE9E3CF3E0 007B8C9F2D934F24D591C330487DDF179CECEC5258C47E4B32538F948AB00673 F9D549C971B0822056B339600FC1E3A5E51844CC8A75B857F15E7276260ED115 C5FD550F53CE5583743B50B0F9B7C4F836DEF6BA1ABE5F0F80D96571277EAF86 A3AAFCE3693728E396048C32573DAA11E6D2F036BD9756F1F0A5877DD15DC64A A9C2E20B570464B31E783692E6D10101828C4F6DF30A155808A7697D24C5854D DD1D111B4B4FE343E045B136706A49E8AE009DC1FB981436DAD464861228DE37 013FFDA371B4DC0BFA7E5D606C9716A66221968F9BC406148F4027AEA6A9DF6B 73B120707CD710D9CF211A1350E1BEEA0D934BED2C0B9092C1264EB98D81C625 4391E134B3A487614CE48710F60DBF482372B2F1B2F0ABF06D6E78D7A18074A8 FD18AF17FC89A5B9DB3DA8FEDFDBE78002D31CA796726FF8870BA31625C90F5A EB380DF50BABF49ABC107690566ECD3AFE5A2D47B79D1FA991F1DCA454619CF7 006240AA135984D97F7EE22C346A97AECECC118DFD8E3D97599B0BAF33D949FE CE 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX8 %!PS-AdobeFont-1.1: CMBX8 1.0 %%CreationDate: 1991 Aug 20 16:36:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 82 /R put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 15 /epsilon1 put dup 22 /mu put dup 23 /nu put dup 27 /sigma put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 114 /r put dup 115 /s put dup 117 /u put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 56 /eight put dup 57 /nine put dup 59 /semicolon put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 35 /numbersign put dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracketrightbigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 22 /macron put dup 35 /numbersign put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 100 /d put dup 105 /i put dup 109 /m put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 8 /circleplus put dup 14 /openbullet put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 25 /approxequal put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 54 /negationslash put dup 59 /emptyset put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H put dup 75 /K put dup 76 /L put dup 78 /N put dup 85 /U put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 77 /M put dup 78 /N put dup 79 /O put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 14 /delta put dup 15 /epsilon1 put dup 17 /eta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 27 /sigma put dup 33 /omega put dup 59 /comma put dup 61 /slash put dup 64 /partialdiff put dup 66 /B put dup 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 76 /L put dup 86 /V put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 63 /perpendicular put dup 67 /C put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 4391C9DF440285B8FC159D0E98D4258FC57892DCC57F7903449E07914FBE9E67 3C15C2153C061EB541F66C11E7EE77D5D77C0B11E1AC55101DA976CCACAB6993 EED1406FBB7FF30EAC9E90B90B2AF4EC7C273CA32F11A5C1426FF641B4A2FB2F 4E68635C93DB835737567FAF8471CBC05078DCD4E40E25A2F4E5AF46C234CF59 2A1CE8F39E1BA1B2A594355637E474167EAD4D97D51AF0A899B44387E1FD933A 323AFDA6BA740534A510B4705C0A15647AFBF3E53A82BF320DD96753639BE49C 2F79A1988863EF977B800C9DB5B42039C23EB86953713F730E03EA22FF7BB2C1 D97D33FD77B1BDCC2A60B12CF7805CFC90C5B914C0F30A673DF9587F93E47CEA 5932DD1930560C4F0D97547BCD805D6D854455B13A4D7382A22F562D7C55041F 0FD294BDAA1834820F894265A667E5C97D95FF152531EF97258F56374502865D A1E7C0C5FB7C6FB7D3C43FEB3431095A59FBF6F61CEC6D6DEE09F4EB0FD70D77 2A8B0A4984C6120293F6B947944BE23259F6EB64303D627353163B6505FC8A60 00681F7A3968B6CBB49E0420A691258F5E7B07B417157803FCBE9B9FB1F80FD8 CA0A265B570BA294792DD2FC75CE2C83DCC225B902551DBD11E687EAC6E85D2B 02C28359A40AE66A6A6A8862CB17815B41E280313F0EFAA9981755611F7F683D 35603984D60BB0C772054355A97A5E03C689E23B04DA79080CE4579CC90EF38B 1A64CDD92B907AE83192C3C46C5FC40BB412F6656DC6349E6D29B5936DCE94CB 98E3B465FFF7574095F57BB3750F1A525FDE28FB8FCA4F0DBD8BF16A3F1FD9A9 CD52473E23A90E6632D39EBD39223004B2382EA7B1CE8E90BE77C69CB5B9F659 009CF2105EBACE0CF9BA0295F1937CDBF7F718B6B85C984490D1E560E9989B89 D7905696D5F64BFD9BA1A7CE898BF3C65F0474C8D72FE45C231EF90C86E14C74 615D2E9A57D848467627807915781EB7E8C0365187776732E23F8DE6B7FF9728 76C4C2526F6C573DA11F7606C5484FB0E9DF7EB39C9BD47B5D0710BDE6BE3B98 0A7ABC119779DFBDF6FD13EED6976950AC4AF5B21906B6E84803AA6C09B3CE6D 39C643F2CAA75C5C740AF5D8B5E7986C19E63C80D648918F1CE878565C67FFA8 DD0B9FA88BE2C1A6D1DEB76710B0BD6E8F75779D73BCB99CD9F05D9F60A92364 C427E3F7CDF9C65F94E887C1E8E92C01FE6E9CAFF32E32E44997F7CBB7FFC71F C82F8D173315A44103BDF547EE0A78E085205665F388085839515F0A04B1BCEF B27355612374EC339DDFEF0101A9CAD4EFEA168F36C057CFCDC2DE5A13ED8810 88B6B60682F4DD99DD79DA90F9F8A854E4C5A61DBF3CCB017E5E35F756077541 F8C5593A7FBE0018B685A34C3C85CEDAABD9BCE6C122D6D987BFA89BC3B9D0B6 3FAD086C7A1C3E4AFA64BD048E47894717902E89688D20129A61E232E64AE833 C10CBCAB3CB33963B19C9FB62E0B300C72B207D05894E3A400CF8B83ECE8517E 1CDFE7A0BB60C5B34A1BFCFA617BF40271ABC2536E1BB3021AA9C6CCA9AD81FA 94AB9D046DBCF69C056045D57B82288F97C5D162A61301D35F1186E2B11BBA73 2BECA0EA73E1EBB920A5D0704BCBE12F991BF7A0CC1AB2AF212F9623831883C9 3110751B5F8127351D17478F20648D81002496E0E1E220852FA8B232CD9570DE D42DAFC584C6C6153D72B476D8B06621615F71BFCDA8D6EB0CC26F5437B1EA2C FCE1E66A2C57714167A1A8C656DC0784518C1BF751880CFD0C6B7DAAA54FF2FF 0FEEFE846C1CA4A8D4EAF4E5CA52AF81F8F896FDEBA7B9076094D099D9F86E5A 8C591967C3CE31F9440DFE3D9C72D58C4E0DE23253AF0DA930D4601BC0E3F2EF E0A988BB92D518F04BCCE1DD5CD980A5C2823A544B62C2BDC5C0566BFE13CE8A 5C91642CFFB4D4FBE79260398A8FBEC2E6CF062D23758992D77E8C9BAD45C53F EFA455B13D02A33AD1B9ABAE77001617758E8C918989620116D308CC9BC8DBD7 67EC033AD5A9D4F2D35DFAF72F5CB5323FFB59AED8D1160A835179E9865AC214 43EE1DEC3A9FE077F292F5FEB254248BD15A43D7AB952C47B176E2928AE2D306 5815B2C7FEF144E149AE59C2ADA49D041B365733179A2986B0FD1F8BBD815CFB AC9294E4234C69D882520B345AE835C767CC9282BB4909D5AC04867120F2EBCE 21786F726B007621074E0E8988D20A531009640AD31408B6D26E3369E24F4C61 636DA460CD2C93DB27F42DD0FBF97B6B9AE10B921E7324CEB0010A83A367CC03 93320AECFE7169A9253C8B1DB89841B0EED6903E8B49E376DF2B4262BF143572 70B540CFC76E6C48D6F47E56C318A4A7DCD3BD49079468BA4BBE6556ED237747 EABB1769D8A8FD5A9C1C997F57FE3DA22ECFB4954984C14D987BFF950F307A07 9A38BBF32A47431001898CC6A71AD9C7D047EE0D0C60C07D0695BFF93B565B03 C4675C9C9060B75A430BD0C75C983F60C1A88F307FBF30853F2F93820E51AABC 0285B0BC21A582483CFDB6BC105C278B8178435046B5A400B3F2D6E48043F4C8 2D0F7DFB3A931F19349BEDD1E3ABCCFAFE7E31AD94D11572FD91E2E7B469AC57 D24094EE01FCAA5B18F275CA9310960930347C0A68448D00D263392C1740DDAA 2FF850E6B38EA34D035D72DE383EEBA2A57D9840B2FAB1D044F64B4ABD5924CE 3EA0C8F6E73A8B926BB3F32440FC0730348718E9953DA77D0961957881AD0767 D8300A7B3EFD1B1F5AF59179A0C7B039369CC7A383A3DC96B2ED782FCCEF0A28 9F55A08A6E07B9B117404807713B37711CD9107A9AC57EDFC81A3EBE0FDB0935 5683DEA4F071353D095DDEDC392DE82969DAF2BD1CCD3166BECCE56D12E87848 D5324E245D1DAC5D4F167F25EC8FC82442E5D5B25E1BB579D448CB6390395363 F6020071F3A6852252644E60CDD359A110430128FFB459A478F50DEB717CF831 C1FE7C68DAF857015336B76947F033FA142525363B2B643309B1E151D5E0369D ADF349541387B6A561A55E89C27509DB12ACD4560D4BDDE3EC00E74F23536C63 87DD510FD500575A91E3140A668C3EC3225C784CE31400A84EC5BC5D78A8EAAE C630C9500F18E2CDFDC8F72B99B6CBE725E3AA79EF0C60B6F9BFF38721024C63 8519E6967BA09C8870A56DAF07D1D8C7D205D6495B88EACBCC11A4D943CEA477 A230F045146EA9FF8492368B285FF7ED3616B588653DD6B1F7CCDEAFBC0D76D4 7CAB4814EB6536DF8127F19D722BB8238A7F6BC6A180ECA0AE896123F9450416 D12AC274AAF13212CA2468E2E963343C94F060058B09428588200B4E61405D75 687990B8B46F27AB6092BB37F4DE712D30A2AC759F203B76949F8DE0AAEF5FE2 E664979BB23E0F8CBF2C9DC07F0A2866B835E7E13BDBCC6DB16730F848AC11D3 E4BD9BDBDBD270522F88E0F6F530E799E404C7FB58754BD9FB6616DDF09D56DF FC31C62B9E90DB0CE68F7AA8423A2C1CED2DE21EA2B9FB8FBC3CA67997C68873 6106F843D704C64147CA0B798B872C00AEDCA639CFEA93CCA1F5E084CD20B547 E2EAE9C8EFCEA02864C04171A90380EFFDB567927EBEAD011DBCD9B9BEA4B884 3BCBE4F283B9E92F89C25D9438B8485FF662AC3159A4D0F6E65E9E2D88D69F2D E0720CCA552536D08DD21ECDB26D636CAE6D96B290AD889AC5FEFEDEB2B2C82A 7D3E59516B69D1FECD9C20AD36D3F3EDE599E21916B3E64EB7C5FA15954F1D34 89B5288FBD481891BA98AD96BE9167C61530554B74A7B28ADD2C5A7E87F54CD7 E088F9D862C0EF85C5B20D54C2EAF25BAE75E59541880607A3178F610C7503AE 8053068B371E6BF62EE3E83A657E08AD1ECF5413CFACBBF4DE214C858B0DC9B9 9CD3799EC6AE59285FD0835A810A06CB31FAE375CE5FB44A1116E594E2918F5F D7FEBC5CB175A48048E05CF61C075BAAC79002FFEECD349D3525417F118B6640 D40128D98A7D6DEEE944EF4DC58ACEE3C697D326967359270992A5F016A2CEC1 E59A4CD196C9EA60C02F18B5DF14A717B6A849FC6DD365FD6FBD034601CCB661 3582812DB19D0552B599539582718EF518BA0785FFCE00ECF5B3F750EEDB2043 CD4B67081851B3DFAE49D391F1C79B82AC628D6B66C2E1BB3CC126D9C33C2EB7 73C7978D4F02A3C1825A424325FA0F374F705EDC396E7DB4B4F3E12F1E7CA6D0 25E9D390558BE804C6A4B6356C3BF442E2B3832FD42264DA93D9B94D2B8F31ED FE9B8B0FE0E0A9EF8098AC7CABE4A03EBBA69CA498F5D511F8B29471267CD78D BEEC78282F1EC4A4D1ACB19871F80DE31CB448CD5BBEE2E011836A667197E10F 2E6E395C9292ECEEEA6C9E4163950FBE5F4ED5BEB7E03264A6D3210182EC4BC8 708024D64E59E442226D6BB176D9527FDCA62BCBF66159BB5888C884E0C57977 E55E19CB73F4569C4394E72B7C5968195B142EA4AEFBA49B13F47F46FAE0EBD5 CFA20E77F288483A12F903DBF7864CAC6BA30648815F4578AB016DFA334B70DF 42C68917C1DE5ED9F98DA6203D75CD774DCA5A63EBC1FA0AA4840DF1CB6E0728 FAEDE8D82B7FB06EBBEDB6B8DF349D4150B2B6FB0AD8EC51C237165C6EC0A6CE 4F072281FE742565E301EF07E6297847C5F4466E6D6BB1155546DC528753CA05 AA0544B1EAD41869CD3D97D54E8CD3E19FC560E12207E4E237F6F37D97F82410 09ED44DC6F3ADC03733C40F0D730593290C413A717F8DBBB7B4949E233874844 D3DBCBB6D5A64E39CF7BC570DAA4C53431A1C81D710CAF4DC62776F5C910228B D446007D106A7B477D7CE2ED65DBDB0CB17F035B9260FFBD63A0EAAFB1C7721B EEB582B0D73E127B77765FD21C5730BA5F6C3BB939B1686AFA686035A230B161 BFAB73EEA28C3A249303AA6432D0A4F354A96C2065FF303CD2D5DCA43DFA02A2 75D85729CFDCB08F8442DA138D5FFB10C6BC903D8873C98E160BD1F769DEF87A 0BDAE170CCB956E1869136C58270BF365C5464E109ADECEE83F390C96B7188C2 88DEC47DD65AAC63FA1975956C2BEC9EBDF99E97638B5318BA4187BC4A593460 1765F89F80BCDB90E8821AB5B72376884123CB57E2BEA30394CE73170FFA3015 D61EE976EFD3D28A2EA543B9E142D900F21B76387329DE1220821E541C8F921B 92119F1BA19CE83BF841EF5F6E347DBF6714BFB37D3D78D4014A4A7E6BDAC5D3 DA7A4168C568C054C1B5833BC652E551F131C8F72A1DA8F9729E09D8B544F64E 51F1773224D4A0A35EB9F68D978762D27BF5D5DC856DE958A0949F5647AA946A F20AEDD907C8779C581851B96258439EB8AB7D35B91CD73C788F7F64E7081B49 F57D0F1C5B47A15D20341A73C44383E731708A85F77451BB23DAFE53BF3E924F 9FE44A450F0EF0F9885B0D58174954F6CB624653B705407F7EC700076387759D FA9DC059F60C933B4A6F3DA8EB68A410349050EDBBFB295F034CDC0C76390146 AB3D6B0874F7CDDDB3F8205DD18698A2F2302B6C60671BC8263104A1B7B02B3D 59D7CBB0E807D49BE903D7C35DA4BFD21DE4E47AF05CDA33E7EA336D92A09D94 7FB201F136C4E22E8B82F8D954E5501B0469440BE489B6FA7BB7EE7176F33D0C FF6086857AB39E2071CCA9EAAB7C338FB4EFAB21C7D937CAE8C4767D39EDA50E 9E27D4DFAB57EFDF87740859591CFFB94E69B66DAF0D46E28395323AD43F6FE9 FD4F0D0DFE068A35C7294A6FC51216216ED1E7369C37CAF14E251D2AAF85AEBB 2B7215C94BCF1FF797C9A77307E9ABB7F0701245C15650F846CEF56041CE387D 42F7AA432D5312D0F677E16A7A26A5946E634EFBA68D65CC56402BD294C7FB61 4105A34F5E2533ABB4B43D2C0746286DF81A7FFB4C28CF2AA2F8B5B14B7119C6 F37487F40C6CE629A9C3F4EB2BFFFA13217241C07A32817F7A55CF135AA87817 FE86DB0260797186AF2A5AE59003E6827B0378B02A50111D6E11635B5A8DFCAA CE9A586C2624F6F78A44107939FA4E79748A75BB6A0E26844D134696DCBA06CF 2918F89B936D9793EBFDEED763446BE7A7F5A999B9EB5F837E4A093F1B348701 FB6D67C76EBFE6BDA231FDDCCA6B14CF21D35674AF14E8796293FE544A58B403 769024E003DDB8B03B1690D90DA2A9F902580FB1FBB9BC48704B1A49D960DBEE 30F161C9DF28D07CAF0A672DFC4AA2B67E5EC1D85C86A0ECB2CEF7539EA3C195 E5B0B7F426B2CFD8B8323F25C3C2D9FE17174E2EDAAD5CC3C5F73CF4B70882A0 24D670B7A0C57F3821F36E307F666F4969C733F9F505115B8989C62D1B630DDC 93240178935326DC22167A6D89EA9A6F1E360A43818B09BF49F37BCF34EEDB6C 9E07CE1FC7F536815FB8EDC4668D648E4E2B5FB3F45D967A9E118F32AF8749EC E825A909E245506F08E0820A2AD4DB22898A8217316ED2E678C477026B07D5D6 04B02B90FF098AFF6142FAC8286C5EF54D4D6ADED3D35DD3CDFA3307E87754C2 DA9AB96D957420CAB156AF655AFEF121043DEF73448B5D57B71BE14EDB13E899 0171FC0730E6D1C8B0637289DFC349D821F8E46578871431E920818C9F9C6C0C 835DB7A005C286F4D290F3DF078B9EC70FD6781771A8960B2E29A54FD5FF9273 0C02B488FE6686C65D627525EC69076FB1606C12CF67F8A4C2693F4BE5E03222 E6325A2D1187C18787620CA60772C4535EF24D00812F98345EFF2CE2F374D2C1 DBF5B857CB385B5BD2626F01B4CBB2B5DC3D1E4F02BA0EBAE11F4BB3353C8099 9EF11D9DF8DDC9B26C6B2AFA42EED3F06AC9534B24A05DF67E4E8E6915A8F4B0 8684014E7D3F2FDB28D8AEAAB427612AD37A6864ADA2420D4FCE3919BC774563 A772620637AB0A3D7760D9692DCD035A22C681D15409B354343FA5E0CF187F3F ACC58DEF24B8009EF195EB865A5EB20C7944D6FB77F4EE43D474E1066A702E7A 0D4AD44696036A8ABD73CDD1DA0D7803C2A34822C85357222E3865907B0A7545 33207472751200FEDEBAA283ED75E617F52D2CEAF58089B610FA60B5FC4BDCE1 E7291694F808CFE55D6EE776E0422E9BD46531E6D787B5D215300660DA21C5B1 331CD7593B84EA301EBFCEFB720672EE1E82203E2F99966228B6F76D6A401CA1 9FB09BD8AB3EEAFD661B291D46CB8EEEE38DE4C481917D51E5A5878630106E63 7C71EE217FB014ECC2DA7F3CC7B5558B26AFA283D9690EEB5F165DDDE7A90838 E996C1C3A4EEBA9731593A6F606D08BB03ACF103D7208EF4F1C0A7CF94A7C306 BDECC6E07842A28F7755128A8E73A394048B3FFD6154B3024ADA52359317863B C6DE3349C6139AD70A4E24177541CB68AD4C34106D5E843BC7F1340CB113FD1A 546F65ED7652CEDEA06147AA959A6E9147E8C2011569675537931C10ED1198CB E319874429BB412D0A58923E358EB6D23BD55057A0FDEA19E2639F364804375A 152DD0983F2DD679B01D0AB52471DD9E1A6CB0B68EA10BB055D51EF11605CE7F 5BCC4CFBA03EE44B17D0ADE55CB66EB97479298EB40596240EDAB9396F1234A8 00FAA8B147917D97ACF21CB5ABBE54EBEEEC192D8D1E7D5700CA2BF5FDDB415B 72547EECCE408683DB9761FFE084CDD2EC7D37AB4F8A576C6D0DFBEA6CA09E25 CE04195A8802D71E48ADB3D9B7E4B56EFC7A6E4E7BABC83B2837F4EFD75DDA3E 6E9BD8551A5139955A4DE9A91238DCB0BEFC2C5A49F7ECE7EB1F18F73629BF0E D7BC90B1C7A74C64DDC86B10D6DA897D5FC4DDD745FAE93F04C9EF769F15DE0D E9F192B6C4666479B9A156E06C740CE2B2FB8A750AC6CE42D8A3BDA594D9D7EF 11F066A1BCD1697DB83CE74A1968DC072CA0274FB30C7B7E6D205D86F6583C07 CFF1427DD93C2D004F9B7A80233D9A9D0D096DE94E7EA5C12169F9B0775748A6 5A74648A05704EF887EB30774CA7A252C2D2BBA103F324B73F7901C44FD87D70 8CF41927B36351D9561FF5A71B514A1591426E54D7A075EDEBDF40166670C9DD A88DEB28D9749A1E3F6D317551E824581F21BB7D0C72F3F621D19431A4AFEDA6 D9435A3EBB477FD4459F0C6457E29003A2A775D747F5977323C53B9F4126EB1C 3A7B40F7F1D835400E99E417080BBBA0EE33FE1D37095C3B33EB9941B47B263A 74E87E6601A5963DDB65E718E03214E15334FBB5384326A0091C3C60180CD61E D3971551C31F63468CE5431B4546CD662A9888C366E145F75111011513034DEB 11C149EA14B2D74F782074CC3674CAD53D318EFDAA1181FA99C519FA190371E4 668023CCE0FD5AC640CD80C932D8C336F6D4E324E3F8F62AAD93ECDF3263C038 01B310BF64A59F1681C0A61C540ECFA0773E0953DB135DDE1DE53F4698AC5930 54224507E9F84F66FF5F87B9A3636F83208E2A7B56709EE4F1668675E453BFB8 8F26BB12E18D94B42561E2BCD1EC5BF5FADFFB875930002B83B52722F55BC6AF A755793D9FC7C3343D40A303B72DEA1B9BDEA3264183FE1C5F5A8616E9AA27FC 8E16C10F704CF5A5FB48FD847259A63B13A89686E4B409CFD356C80E12C8003A 127BE4D00C156DD4C287847607A28F02FD2B739E7507095E0670BA3FB45F622C 1CB6CBE6562BDDE69D97A99A444A7245F5FDFCA8CC7B0D67726486F6E3E71AE4 5147866D56CCB0769220E887AF8E41C29F4C23ECC637F8EF6A1429A7794B6171 4F2D674373719FD40937E768CADAF952D869254C21C634F02EA121BC205C88FE FB5C45A7E048EE2FA71D0F7CBD7A1EC919AE2240698808B12CEC0D32FFA952A7 BC92C4AD3E302B66F5E501B30BADDBE9D8C1C6738FCEADC873DE5A3D7B3707E1 9B94B971D293B364BA5869AF4801B1CD33890E902DA0949EB90DB54B9E150998 21F7929C1685BBA02B8CC53EB207BA6440DA84C49215395F2007E7B698898BE0 072AFBA6C5854E77E99480B7F08A4F31D490E81028B391BB4C74FF5C18FF28E6 13711226C35229F8736F333A6D6647EA2F200BEF509B84EE43A9A5516D3DEFEB B6C9C73502EA2E185A29946B4927E9A4C42E7072ED597B3221F162C98CAA9313 87F1875E863D65D50D4614CBD0649172D20C55509C91718D7AACF5A208961326 D0C0466D27F7AE44AA5549E26003004CDDD056CC02362FA167BBE11052D0CCE7 9D78DE7979573E8C4FB19121CE77D0562F4E4E10A6D5D00C31B145539F53D571 8AEE4F03AD68C6258B300785E49F2F8368509D14DE3FEA30670E0C2F0CF104CE F4EC8FAE8F83500692D08F80F21785FD8FAF6809AD1C01480CEC5955F03E4EAB 9E2D3CE4DA20F3C0D8749EE2D0086545A388EEBBB6855BA4020153F9DF7A2A2D FA080F16F87D6C7C8F57DB21F79CF4FC945A4EDD727FB0553B91F3F58B4B8016 12058261AD38978C0B9E5D21A3389330CFB7B468905765E0B4120B277C201F6D 9ACFDB150AA464A7279EEBCBB2AABE0C21E94E26E2EFA104BAECACFFD986B044 A9B9DF404814F1806449809954C28562E7ACF5619D3D624A04EBBD08853F67F9 A59C7200AE5BF620407462AB66385CC79F26DCC1F2A7CBFD1BD9C1CF4C5A2AF8 712B1D2A55C3CB94DC3E99650FE74E2FDFCA40C3BD2994FB8B559CA7B901C4D4 99E87C474E5DA4051D841C231887466544A27486106F587D109174BCA564C98E DB232FF4066E1F0E2DB06B50208E8F07EC2ADC29B1DFEB51291CB120B71B1B67 050C99BDC74B3DD40B0FD50D3071D10C3F92432F058E707DD05B2AAB6B41C39F EA70BE42AE60E18BB224F6CA7E150E6EF5A6C105AE4048F1FFFE3DEDA6D3F3A0 EE3B749227EE5DD98946F138F2F54B989B62A2DD3F1D3B2D0E51DAEE34FFD343 417B798C88B65284CCF9313543D7A0A1B90C87DABA341F29F93571623CCCBA6E 382DF4EEF88151E23FC92EF41987C1CB6DA272B7D9EA6A88B621615D94606B41 908B526DCCBD3D0F65871682D9DF92296FF58829AE44F913AF942C46DE9B2CCA 3092D0DAD37C7FE07460262D6A02C403654840C4E77713D4D35DA22A1DF9454D DBF43E8E564C188B074E609B27AC406B6353B44626E34D4FD08660F16A1E1FEF CE4DBD9CCB31CDB544A02995C9FA0F0DEEEC3759685B0C370F8895C3A2C8CA3D DC0635C498CD72C842F16852E7B7DA507EDD58B2D9675E85F9E5EDE26A6E1F63 C2C7BA36C115DB18EA981FE1205E77A210907D281BD9269D5C3105883569B4B0 3E5F4BD6C7C155C97E1C53A1F2923513A734BD1ABC4B291D2FE2A2F47046D447 4B8DF690B06DE1097CEF98FBF8BABF0C8F378943927B157AFD8A7EE977713547 A983F989D7E400A64A4BEFEF19652E94C918986AD8B8D8DE796C7EF1E467A23C 833DBBF87E2D6C6EDC47167B59CF9CC828EF4329C35ACB1892643F8A9656D594 F030BC836122E1F2416ECE61D175F69D62595A60CB4D901781E32C38A4EC5866 D6C11A13A240B3137F317792112F7C0CFBBF0595C29CB9A6E63C8359A131662F 86BD7440D7D64B9888B989D33FE3E4B20CFC6EAE06858C602790D293A0140675 1D9E74F63E92A7B914FE28A8D3B3E544DCC37217D371EEF609998C9758021E08 DAFFD30E0A0FA7C2EA9C0862D7DB3D6596706371E51F7C71B89A05EBFCE17ADE CD5FFAA73214F232E2F703395E483CC3A01CA87EA43435647D76C76D697C267B C1686352BC80B31F6BF4E6000946379170159DBE548B5CEE9343F18965135798 A3839FFBB5462C354B02CFDE53DE5A82C11C70850C3C2959FD14AB944FA128F1 AB76A145A092E5D23E445CE6E86A5AFA2DFE2503FD669FF35FCCD29AE6F80011 2B3EE5FE4B931A3EBD6B1EED5F57ACED4CD629342CA0717098325BEC3520F343 69145A1C3437F1C46C14FE7D697A4E8791D279A1E62ADB74B86E56C731EEFBF0 EDFB57ECDAE411A65960020E03AC600A20CEA92B438554B358173D1BBD7124EB 11916F1B752E6660BF2F86BBBED90BAAA0A2AF2E8461CE51719CE6EAA87BFFA1 C4DD4124247E9F8B999EF64BA207FDF233BFCFC5B8D059C7190FD9ACBB8377D9 1912065F4D2A80104F617FFB1DFC6FFC9F7D5FF6CA1A8D8CC7A4013B9106BC93 08882E42E8ABB8DCB9D45DA3C08297EBB060791546C544DFF723F9971560AD5A D6B397603017269C38F3A1961C665AB95EFA55442FA48D51453EFDE447C1499B AC595BD8D3B3CF2E1554D92D97064AF82490C3350EB7B87287EC3C12EAF5CE58 BA3889700A4D56D78B657B4A43F0B401492E1EE3B160E7B1F24CFB48004149A7 FB1862FD00708F24FC62C69DBAE277E15AC94B24EEE40C88D1E1D61A8266D1A4 680589A22AFB4EB4E88FCC5F2B7F27E4ABD9C3CBB0825E445F8C4B3EEAF8A72C 03CECEF7B917B36955CB0149F0D389FF9483C03B8B3874E776A27D2565A0F10C 49D8C054650EE00AD2D2A04D84FE283BE76F89A81A42F0FB044BF393E533D946 6AAFE02E3816900099E3580EA22C37D428AEE135B580AEDE8F14D12E8005D8C8 0AC7AE6A52CFF85A93A16DAFEB98B280A59D47D601CF652A7D1F81FA5F4F7F66 B540DE2B69C847593B4646F99A38DB69E24F21C2855851459A9AAE606AD8BCA4 8624852601AC7C8B1184F6D787AA0D10ED0AA373A925AAA6F6059DF04ECAC43D D60F5E8D69FE4A28D64ABC8CCC97F998333E83A0CFBA65E32B4A074FF0C9E356 FB887637EB48981F643CDA7AD5D1411BFC7C4A6FFF62498C859B385DCB2F4821 B35F7D6DDDBB0E8B6FF6FBD99BE896DF3BA14EB65A6A2BECDB85893CD8DBC185 79817AD384B721DEC9FA84566F85A386BFCE82BBC1F992EB388BA7C3BC75EF61 1FAD965CD9DBA473926227840AC2D197C1C528140631E9501033844781F79599 7CDF28EF817CFF136DF752843A355FF06F879A4C92A8FAA9EA5FAFFC250D20A4 22E23BAA26FB2985A4A7EAD5B6F7DAEE555782E787967841C9546858202FFF0E 3216DA4AB84706E34EA2940A24CC9F584DED0CBC87449DB5196C1A48965331BC C356CE92819D3E1729946D2F475E82440C5A91C0F6037E86189B265588C8A33B 29F4F39A29E66EB8AEB423CDCE685A834ECFE199E5B6706236BEB247598C4E01 351B7D7FD46193FD181746116F44DF5AAFC426D7BAB29E542720ED8C4585FFF9 20C3DEF85350D6BFA08258D3F5DD469365D27CF4D5C86B6DA2A46F73CC8AD9DE 959605AACB36036822354DC9EB318E1FA2F48710AAD1B3F62E8DFDE23324499F 8FB6E2EA0DDC5854C3FBDC53AF9FA42A4FD1C5EA4371C015487A63716CAD63B2 287769119F8FD981AD08600EC4C082C799BBAF005E2BF1A5943E2DA3A7D42BBE FEBA2617DAAC7C05740C170BC5179A91792CC367F449DFBD8BC03F6F0C242F46 AE42CE0C47E70EF110065A85430EE40121751EB30D2F316E4CBDDAF9319C52D1 909532AE38A089CC6A9E352A3E1CCEC0CB7F0D52C7A3115840FFA9B71C574A9B F8E46AD69E376324C2FC1B86C01A3997FC885523D340947E2102557664724674 FCB5C857C6F5E60E0EF6EFB09F860B58C857B52DDAB7F9314EC46932148D2873 A9BE6F0FA3BE622AFD7EC9FE3F13E9251D0D96339F0F5BA6CE2318A8E5310976 F849CFD8FC4158897DEFBAED2231ABC34A2473A64C33225C756E1CF1622384B8 5D48C508A0AF197E3A522796A0F1F54D3FA291646632AABAA8810E540A640A11 4F174819ED3430794EB2A2496955FCBEE37C0094CC21D03C5FA3090E2C01DC77 C584A21600F6C245648E7DFFA75ED007DE9738E8717F3ECF275BD5A6515000B6 816F5F4B2626644EE7C101A98EC812F97CC2131796C3449786502A8990D48712 13963E0146A431C5E50E9E43077FCED1CDA00BEBE048C33C7261B0D2B9758FE5 A4468DD9E6B4AC62B92CDF9EE836D04915BF4CC88E33FD5DCD91C6EF0F3DCF88 03472D82CA1188E9CFB58360E28D679702876B682B78EE71D3DF1C65D5D60E20 9E70EF8F9CB29D001359DF05906871435D687B6D736BD909DB896F0AF77BB35E 49E5AC9A06F1996F42A96DAAA64E4EF88D44262953209CDE15520C5490F27F69 17C501A026CCD87DA47EB06C5F08FA8EA2ABCA9EEC1C3EE798958416FF31264E 9DA2CE9695ADFE364E53E597216A24E5FB0BD6E11C4086928D813581B97EB878 4BA45D6F7E191EB5A6B44BDE2DD2566015A1C0536F5F0B8ADD4834C66E07E80D EF53A28E214DAFCAE6C7DC134D0EC9F06AD7A0BC73E7323027800A2004679148 58F86DCF6328828BD63E217D1C53FDC557D440645FAC3162F4BB6538DCEEDEC3 F7EA3F02781D3DF48CB5EF748EF7D976E7B3E66A1AFAFDADE04AA84FCE6E1A77 B03D7B17BB0F556DAF2B495DA28C1AE651F8C86600AA716EF4691F108AA966D6 CE3FE09933E598D3F090911199A626654AA0392F60A5A4C29A2AF412ADB3C370 42ED8CB600FF036C0E217B2714AF4615BB2F8E7F78DB901BA00BC2EDA6F69C52 B2D7E7E2A41EBF8606D0B6C3469DB5AB0D3487D04CF11DA7F952FE3B2AD98431 FAA645E69CA1A80E36D67C66D13671F65B46E5C1458C17F034A9FF71B1AEBC75 469DCF49530E80736F4011BEECC07A087C5EE3DCC258D97FB2AA8909EB3C800A F043049200BC66C7652AF63FFFE132CB049C0A1F5FD2F6361238E7838579EDFB 06930EF5FF9D2928CFB0BF472D3919CECA5D66AE41F15397EF7DA892D84C32F4 BBF26D3F98BD9E966F94C5388A68856DA082081512E4D5F49C939DE356731D21 803E0F4D8C4111149CD35895C8658110251576E34EAFF58D0A8B1FA5C6540B5B 3B8574C5B4F3C7F3B3EEBAEA28C5F687D6B2A9117120226E7E126E0D54D92E2F 1E435308B222B2F81D1ADF8E52BDC521FC937DCCD1B22EFB45DCCD3611F23E15 AF288D7EF544A2EC5DF7EBB1D79FF4A42429B370FF804401AB2CD7C9BAE54DD7 2679D5BA2550BFD59487A1C498D9901ED4DDEAB73148005D0762489716A142EA 6ABD1EF2C624B5A163C0AF0D1357D4A4DEBAE91F5BA3658061ACF8CAB5C9A9F7 6316CCA91FB5589208A286E4008194C3BB11BC32136C2B4366EC301C481CA7F9 D6ED26CB278DBE47CF79FE9DAFE7645BB24BED1A1CA75447710EAA5C3D81D521 C553F366781AA542E3D855AC189B0BF745C0B8B75E36C9DCE2C7ACE8CD2110A0 14C405873F54AA4FC952DBE92DEDFCAB0505FCE0522B374DCAC022D7C675CF3B C6A9DF179F5A89B8DED84FAC6C921DA23A276C969C5EE71C244A002AB3FD959B 4B921FBFAA725F72989266E8473F3AF688BDA224613DF27450912FC3DE33B690 184AC1F1D14871A9F43DD43D8B807A199998318DC05D066854A69999EAA75094 D9F07293C3D80E9693BC4A62C73B12A5538420DFF30518BD6D5845EC7C1335EF 1073BCFC1123A6DEA01FC6B452F32346E9D6DF992B27BC8BB20923C1BDC9CA43 5F5595325470E44351317CDEF37D9E18DB454216683850BF78E157B299F4380B 690F5899EEC2AB2A4EA3DC857BCAA7902D2DD9FEAF2109D540A2570E361F16E9 3DFAFEA61312DFA34F1B0E179095D2724F23C3369FDF29E3FF876A4538E22C48 43F5BC0BD0D69FCCB214E005FB0F5CE566BCD13977D5A159835B3250610425C2 00B27819CA048D0728FF2267B850D6B092C131ED8AF1726BF12AEF7721F3CADE F2B502F56406EC51DF1ABC8F0E5D5991B836954D2C54EDD0EFF2F4B16D7F08EF 848E9B6380CAC5523BFCBF8CA5C59CBF5CAB933918048D9BD79ACB339DD82383 CBDC35FA6456C06131C1CDB4CD26F4CE8DBE6A829232CDAF589DF73881DADF1E 38E29C5EECF7A246D86247E7DDEC2EBA78A7095181CEBEAE335BA995F570F50F FB65C04153AEB3499D59A6E6A2A04F9605E03FF0D60EBD7DB37A1A73F3FFEAE1 8C03B143C0E82F536ED4D9DCCFC787449FB195556FBBFEEED3EB6E65F134850D EA5264C29382DEAA34CB978182462E11673BB53418954DBD6F0FC05A7D70FE60 D2A59B7E15B97B4037D06A21DD459A78DB7356B3D7E79F46E22F63E220BCDB0A 9F94981C0034F16C8EEB19F954B5E9155A30E7E2862310B00AB7A0FA42FEB5A3 81759DDACC11019B90B51BDFB4EABCDDA0917EB8762FB3B957E9AA3E6F1EAA5F E557DC8696C1EB552E34177575900246EBCF413786054CF64FA6CF9314805A15 D9103BC7BA0E33951FE608738B8FCB5D95F956FED1C819F2BE1459C891AA01B7 A6D60AEBC22BB8BF062D3CF9F88CF24318334B8FAF807E710193B18DB3FD2232 6CD8E246D26E9F4C0CEE492F969D77A0538A8169BF7B60A0F13666FFB68D32AC 69BB84D6874E9186D9CC96787AD77639EAF48B5C7C097428CB50EC6F7C61619D EB6BF48C451ACC2D43E30568DB30F765DAA54934223202553EE0F85E68B9A91C EB5FA293318F30BABA353A4DDC5AAED4B40AAD3267C9817B5FA13D76FCAB4D7E 4E7BB19DE87FEBB123B9517FB10DC0507D0021501404C8157EDFF6EA227CAC11 82142F09D8A015B9677C9EBD5408EBC0E7C742657938CF4529F715AD2DC8332E 079092B70A64F81BABE9EC056E44778111889722182935BE19F7490DE19D685C F449A8CDEB9B26A84E8984AACCB9A4D258230A2E600814EEB12523ABE8E46B6E 1902427973E7B86EF9912E0D024E9BC235FB01EDB0BC00FD2A60975C60A3A567 67160684385222D2FB3E33C69398E35ADB1F57B484520E76B8CA9EFD5D1CBCE4 1586C182E9C06851C185F2631352BECBBC5733A21162D434B10586AB8E68BE31 39D3838A67113E72AEDF9F3BE8BC1D0F8A2E9974BD8DE237DE80C4A89645F882 34E31931C7EA68A7E790BE107A2789ED12A98FE42BF8BDDE7BFCF702A1ECE877 CE4290FF62ADC5BCD6040801BDB35D8E11621349A0DC13C6A7604307AD9E8403 7C248F9D06D9AB614A975E2B7D9076C5533941A5E1B32F99B142B6F0F829A8E7 497351E69469BD1CD540221CBD61003FE3F8D300B48AC0FF264C49D9C0880D0F C67AE3E239F790E45664F68C5C95ECFA3F3ECC730ECBFB4BC594D23A70E255F7 572CD1A8A507F26636DB2DDD532C48E62CE3102F2637F28525774D1238700193 451D9A001FA19E70A1BF0B9158BE827684DE55835191DFA96AFE6C5B3CB15030 B529E35A9C599B1D3A40D21422956B0BA5BBA62602F621B07D495CD5741A59EB 71A3A004DF540934F1E1032A1CD45F5E0E126B838DF20DBA8CADCDA52FBD8CE6 0A3DC035F2C2F29DECF2CCAA3EB2C5C82C651A968C299A3662D4727923458272 19C3E8A3AFA66D19099E301791CB08FE228128535976B238A939BBE6D6546CAA 39C9B2700E7EC6A0194CB0CBCAFCC91E013CF47A7163D2E8CD32AA524385A5AC B1013A7B08597205B55A80979AB941D672EC7F047398A9EDDA598C057E23375D AE19FE89E25A48DA8533B25A3BE1BF95B054300B79503E7926FCC7F9C1DDB18C 6C2A2225A34C555F11127F39FEBD5B3F09EA49CB7AC3F0598CAD6041A8512E79 221C0436F5895521CACFFD806B58A2477997C80F567EF33089269DE1BD448791 841DCCE83DA259ECB05B2A42728D5759E466418329CB79097DA72C8511001E06 4158AC5AA046835169306FEA9B77C96CB77AEE33A56E73FB62B3683E167AEE40 68A2742AF80AA7B45F67E1A6D8E97F38084F8DF88A3192BDEF4880FEE26316FB 02619AA38B80F70EFD58A0F103AD92BF1FE2588DA5F32D74E0948C818BB39479 BE8D73B9580EF83A8281252A175240697D6FF4C2AD2591E76166E5AC67F1D7B3 CBCFEAC394C778B18A7CBFD83D4DF594632B2551DAC9A5C5C4A01DE3379221BE B703146C2BA8E67DE8336D17D1479229DFC940B17C046716DEEB34D9345B5532 F96ACAA33A6F74052E8D44AA18B92E0B05D27701DA59393CC1A78B9D44783E82 AF94FE8D31F3342444778FB19D19C54FE2052BD237BEC2C765E2ABCCA1759E01 0D638A4CB6D28F264F07FE265A37F59FDB31D502A8BD1B4BE52AE1A6ABC508D5 A028FB52D0C82363AEF89C27C46BCEA777C6620D2E136008C7AA3EDF7B7FD9F7 838E0DF14ED2448B0E6C6C35C6B64E1F89BB1D3311EF8BC2AD4B4C56FA2C6C5A 891EAC268139D330C8E7CA81F60D2E4B9F033E83F1C905B4175AA46DACFD0551 B1CE4DC274965361C91DD10476D8DE1F87EAF2CE3F1B391E6EC9669DF533604E CDB9C5CBCFE595C0B234C100A7A4796F43852CABB3258F7D29F00949E0934E4A 3C204468905D6D365F4BCFC9094B9355C03AB69A45CF7924F927447BE61B12F9 410EE0671AC5F6D30E1BAF3D7FCE6D71A4806D9B5C353FBB80DE3399CEB418FA EF99BF9DDB551A436460EBCFDE45D85DEF7D93124BFC15D3E44730ECB079791A BE99321B3471A5C64B67263DADDA07A568667883DE86385F4F290B134908F744 2ED50C512ED717F420E8EF2742DCBACDE10C1C3A75E9DD2F1F49AA09B09F66EB 1B3234123CA99E649F45541BFAA918128B3FB37B2380264BF3F840FAF1390DBA A9DC2F042C7418332DFBF710D948E3FC9E1C6A0662A390318A3AFF91F7598C5D 6B67A7F537A870447912D1ACD51FD63CF61C568E3A63ACD416DF58AE53BB68C6 D7116346E036F67C6440E8FA8758BB056ADDC7A9077548766FB6061FECAA9F0F 82E0B9F450B538872B5D933812D49C84F0CA8FAF443BB85474191D1A26944BD1 79195E4602A142B6E845078929DBCE3FC871D8E8CB1C208F56B20BAC0972A3C7 750D5F5772111F7675831E85944001B0E31F778D4F0A21C0CC9AB74DAB6694F0 BB6B5F070FBEE943CE0F8EEFB68ED9199F2375D4C5074D1D3BF438A0E3EA8EF3 EAB91348E35762AA12A4069B674C95DEEF0701FE2DE56C6A74CEB0E9EF831A38 7E62C7BFF791EA79B1BEF2215136E824164A7A27F5DC1DBE9376D30A18184426 EA2BCA149A97C1E17F3DA68CE4690B8507B3CFDB8FDC3DB9E85C5A6D51D51266 DB78C318162EC71D1DFFAB7121DF8B419B6F9AADCCED4E0332B48317A9DA2E44 D53C71C2C7A852FCB10B4C94D85F74BD579EE3794DFAD331F145D3A13769202B B9682757E1112AE00CE0147ABDDFE16F1745D3514AB90D1658F508DF6E76E10D 17CE87508217A068BEA98DBAA4832D8F1BD24A1EC07FF4B099EA9300F96FFB61 539580B6CAE5E737747F2052BCC78C190E78E779FE6B6EF6B551579D3A22C8DF 22F0B3B1C6C0F8D13518F71C5D66C4CD736E2DD17685BF9BEB131745D1579420 FEEF582AB590C00E1425DF7E2FC77FFA4ED9A7E19C9C595B4FD74949D650C058 402D388E65019D9EBD085FBB7EB04301EE3A922BE415AF773D2F947848F0C68E 1ADB42B641BD583FE510350D1FC8B64C92719E0B4429400EF6145F5796C46FFC C416102EC939ADC84DA9EEC255ACF7DC0443CF8B69D9FE3B696AE296C63131EE DBF7C3525197712A0A8D65C4CB2412F4E3F9512AE3B4EAD6B1E0095804C12560 F6D45CC761F8291BA62C725D6E06D273A263ED66284F11F02328087EB9D0CF44 1D0B9013F9D4397C885193AEB5AB677F12CFB9A2534BACFB7054E6FFD7E405EE 522C72ADE8EF50D0442C3EE98C335570EF4BAEC7AE4939B48244A9E161C8E3DD C4AF8FEE24408FCB1470C42B63C5C4C21B3FDE89BAC25FD446E87E613AD34886 76FBCED66697592010B77B13A6C2AEE0437E87F2A940BBD819AF7B35C1D95C34 645A2809C92F5DED35D53352BE69A7733BD0121F93B21AA14E98E9D407D99D0D EE19B1B30A4F5AA256B11E8D598FA21A7ECAD6501E50B00E3ACB0F0B7C3B0D24 68454B0A98B9984726D094488E6C891C0BAA6F3DA1BEF9C66F8FF22E1B00CEA6 17D31D6BCED21DB860C3F617FB823B4CD5FDF74A94EC67026FB229072DE9E5BF 6E9CA78FA967CB8CB7C1C0FF3F1E110DBABD0C02D1AF7DC7C2968763C633B590 DD99248FF0308127B365FFB68AEE57FC83015257FB8359ACE5D270FCF5CFE856 30CD75DF99D1E8AEE200637B6EBABA4CE3B3B6BA2F1DE8BF83E05AA079BD87BB 02E42C9316DBF7A9CBBBD9238020F0EDAA976C491F183628DF0F3969AE8EB2C4 936688051CF2E734D6ADC36182E346FC0B84E59BA4C42A65ED225AD87E763E52 69927347990465379ECED34A594A1073A5977EC3108511D8F5830BA69CEE1A7A D68C1EE26633D90CFBA3501F2E8DF3E428FEB5B30D2D81CF55632AACDF96569B EFC3F6124656688BD3169D010ED60C62320D29A68D18BAE21562E4CACD4AB2EE F2CF31DDDEA03C72281290E051BAB70AF5BDD09F0E8083A8A5A4E2757A4FFAB2 6A143746E50F1789E85E86D1C514C893D31A9DC487327A83D587A78478711C9C 73D3A80875AA01AE80528557952D618D376EA717808021835D18ACDF1F6FD75C 4DEFFD19CDEDC037BC8A8934645381FDA29DC7B203C0B30D3DC331E461A38422 0EC63830212FDCB1ADA7F73608227A83151F20F0497646517B5A6907A0F5A89E E1BC5B3794987867E29F8615CF1357F99FC10712E6C31A4CE271E587C1075F84 EC60C1CC97CC1ACE645E52974BFC6F229AD229FE82BCF48F18D4EED79429FCDB 99D400322DE6B9FD347717F94BFA31E91297A1AE13AA664995F46608FFF58E14 7B3A01A8ECE56E81D5AF3D82C6F95545C3661681C5CA3E0E34B71C5FBF8ECAA3 3D50ACFF5A4BFDBFB1A1145AF101EE25BCC8FC94AC648F9C2B488C5EAA149FFE C8CBD975B1214DA16786F6568CA8D79C395AFDFD6C005120FBAAE0D9001E1A09 7346C8BF9481D3F0E4E1CE93D32732B2F975A938096EE04865C77C9257BD60DB 3E8ACBC4D6C6E2DD3252FA8EE3B56A69DE0F9DDDE0973275A0614C1179F57D85 A85B7756D5B894FBAB5CA41222D7DEB70336BEE161569BC56736131C3BA25965 416F1991FAD8CBD4DF0A9A38772A8F3A94531676A82F1E0A91DF3E7A54D91714 8AE2E957E94601CADB828C975254EEEF09F3C4D7BF3CE2B5E9DB57EB28CC14AE B2772D96C48B2EA99A486BC123BD4E9F23BC3CFF661C2700F9C908B26006B5A2 5F4456FCCED35351073EF5A086DBD4B154BB810F5DCCF08D8678F1F178230D3C 5DD7CCEA13D28512912DB6FBB64DE3C370620A65DCDAB49CD285959645A20B8E F0CBE517E051D963B169D9C9EBFE13898AE5A61EF5D9E7C3DDC528829C7CAE83 29538D0BCB933471DBA64F50E9F99E32C06891425ED35878911A091B4842B97E 3DEAA5347B33E59B0DC26377C4B19362EAAFD55B94CFD641E97FED8F153716E7 06FBE8617FCF1B948D64A28C0EDC6DE056B0F7848DF76D930618E02C5581918A 3792502ADA87DA751958D397E934416DC50F171CD891A749EF01035F6227FB81 A55A2489CB0B0AF5E7AB1A3D24F8F3D988E24394A7A8CEF5A9823D82CCF2ED86 50A4F2E56293DD9F8853989B41B2477827CA40389AF450EDD8513F8FC667E78E D1D27673379E8CBBAED157159CF0E0853C765E08D34152A58A9DE006DC894CB2 F987A004CC27B1FD288620D71C7CCFF15E90EFD76A40B3AF21099B67D8424549 E09F3DCA7EF37CD389E20FC7BE5AF943537217C1044FE6546E001C45F23D6C50 2CFD1C317FDE767071365397270AED63E3477FAF10F2F72497D523AEEDDBCBC7 FC272C31E05A21EBBED9220254F6C81BCAC355257F8D8EFFED54153B28928822 861870AB07A669E44FC1610CDE7E7EB43123B3E82CAC77097A4B8CFCB3EA835F 1783D37A076E7362F42035EA660BAC613F16C4512761E375ED5694B6E18130B4 94D9B10CEF711D2E677A28D2DFBD28176FD5B6F449CD5A76663D8B19E905905E BBAB9C037F86CB9766224DF7D8E4A88051455C5AE6A1B2B3C7BCB3D2DA6DD72C 1ADD0479CFB9F5457EC778D62CD8D8E62EB0311CD7F4DAC1424C516B78288748 0D0040157630ACC0C12998E8E5960D66C602C76F746F07F34DFFCCF05A4ABBC4 5722BF328F8854D770DF77DE00CF28D14C9CDDCE830C2A846BE2239AF972B608 8EE2DDF5A6344CA43D214CD741F7DB3B3C9399F2A1D3A75A8B01A6662D9C5320 40DC430C18F7E77F3B8754E63EC11481D5EFFE24FF6CD8DAB0CD08D893DDD891 77001ED6E9356A6CA08E998247DDDAD60D67B00366BC1D79BF8E79435BD0AD18 D8138E1DCB0C33A338E90DA8715A3F6A68E4D40C30B0B147947F8637352D10BF 94936A245ADF9055CB806A2E8A66935B60D81D850E00166D1545D09A4A988211 13B643B982E98735166EB3E5FA6746686A251E7A0B284048EF6F96A537E75AB9 2FB5B1F9B90635CB980185644ABB692C0B0662ABC7582A501F20295B233E1A5B C2568EFB17D5A4DD4CBC72225650E020DDD27A8844F143D2AE995A71BE46C406 3816E544700E5D87696CF878D9722A39223A0E21CCF7970F8C9E0C14D4F9D95F 74E1481B45C91008A76F996E4768E68081B06DC4AC964F42D6B742DDD7BFBDD2 E4D5AA66088732FC69A95D510653F24CD09A1DF79BFEE1588733B74C1EFF2938 673D85EE27BFC9EE4585D075AAF2A8E6ED795345C0DA67DF24396407FDF798EF 56C84ADC6F8AA6B1D967A9B6AFD0F8BF1A4BFAEF4A256E592000A54DDB2E38C0 B8C6370C6F493B98EAF3C6ADD21BC5E599814C694122A8042C8BC40F47D37E90 4E3677FEE6DF5B3E0DF5D3A83E04759FF434FB8F8AF57FC53ECDD2DAC2705214 3A91800E8A9E4C3D78DBAEB42639807D97AE1D572691D1AF97F632D5DF8AD77C DC19BF8C3CB297DF5449730FFB0B63B46C23BA44E0B8E9ECC15DE8DAA44BBFC5 9FB56C825BA67471D9BA614FD03EBD6ADEFA4D6807EB49D6D8D13F1782B90A2A 42E3B281461103C4F7AA61A63C3BF1ECD653DEFC169C36FC8C2DDA9F48E10A53 5C092F46866012FB5CFA8B369164B936F617028C41CE72570E2FEA86FE253324 3060975F04B65D254D849729F82FA83ACD35A02B71FFD12BFA8684EA5219AD51 6271E474942970524CCD825A8E7C839E754D3C793B8860CFD9AE60AF313993AF 27D830575A59F9EE8805256811CBE189D6B5645B7086400DF8B1BF997BA58FAF 9D00016C81A0048939306739B8EE2D782324DE7A542052A14279ECD0D8522E54 ED4D43DF93DDD0D95BA919103E15C2DB92FD18E509E4C26BDB0D11B89A275B65 55B366D06B0FBF4819D6641222438EB7516969C670FEF28318E03219E145FD4E 9E47AE0A93ECFFA5C104CD63532D848EFBE916B1FFEF0E00233C9E5D691D45CB 0DC891CFAC583DF501AF717804FC83267134929C68417BD37B56B544B4C10744 85D3B8472062F87893283DC9155CBB86C731E57B3A367DCCFC9E67E1AF8A7BD3 3080B83C52202B979B3A428FF8656064EDCBA81A284EA0817425EEC3BDF6A8CE 955C587D62F27FC732F6942089341E68E2481E996E89DE79F78E89C06877CF94 609684B356DF1CA3099DD1CF06E8412EE5429AAF95D40B8D22C493B14756937D AD1A8F8301133941CB6E6F34B2553C5A7B07C0AFF07F114055929D82A44C1F37 3F4381D1AF583638A3199ABA8C3B0E6FC40DCBE623E96F99C265BCE71D81C5D6 3FA400986E55A98AE0D755373429DF04BEF83752E2CB5BFD23314B69E7A91080 2A0E51A5EBEBA182D3782DAE8F913FB6855D56C3CE756BF12CD6CBAE40181C6F 675205C452D3F34088E6C7546817DBEF32AEE822022926EC3FA0F1FCCE02F620 9AE09BC5C294058FF65E66D5878CBBEC729476B911FD325B9DD80F15B810FB7D 0047B292B14E47D247124E265BD2287A0A7911940CEE79624131D74E7AA98F11 2E2ADB615E005EDE5191BCA5BA6D3E1AD1C3406CE19117966CA07640437AE367 AC6EA3612443F5EB389982012484E9D1BA21DC98A169B9FBA8C55FB265CEA455 7080A225AD5D04CE4DBFA972DCA8050C595EDA3AD8A03BCF26A9B66BFA925358 75126F26ABFCDFC142F826E001921D399CA836013F07B21B04BA145899AE6791 B88ED4E2058766E1CD67A91885DCE118AB27B9634626D59D692C03B660F06B82 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 8 /Phi put dup 9 /Psi put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 21 /breve put dup 22 /macron put dup 28 /oslash put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA04C77322EB2E6A79D73DC194E 59C120A2DABB9BF72E2CF256DD6EB54EECBA588101ABD933B57CE8A3A0D16B28 51D7494F73096DF53BDC66BBF896B587DF9643317D5F610CD9088F9849126F23 DDE030F7B277DD99055C8B119CAE9C99158AC4E150CDFC2C66ED92EBB4CC092A AA078CE16247A1335AD332DAA950D20395A7384C33FF72EAA31A5B89766E635F 45C4C068AD7EE867398F0381B07CB94D29FF097D59FF9961D195A948E3D87C31 821E9295A56D21875B41988F7A16A1587050C3C71B4E4355BB37F255D6B237CE 96F25467F70FA19E0F85785FF49068949CCC79F2F8AE57D5F79BB9C5CF5EED5D 9857B9967D9B96CDCF73D5D65FF75AFABB66734018BAE264597220C89FD17379 26764A9302D078B4EB0E29178C878FD61007EEA2DDB119AE88C57ECFEF4B71E4 140A34951DDC3568A84CC92371A789021A103A1A347050FDA6ECF7903F67D213 1D0C7C474A9053866E9C88E65E6932BA87A73686EAB0019389F84D159809C498 1E7A30ED942EB211B00DBFF5BCC720F4E276C3339B31B6EABBB078430E6A09BB 377D3061A20B1EB98796B8607EECBC699445EAA866C38E03ED7D4F3EDBCA1926 2AF6A41F67AFCFBF3630C943FA111E4CCD988A7363F7C2B75EAF5830B049460E 0D2B337988F150B9182E989E7750C51BA83DF37685483F86D1F47478883F3F6A 4B7F768DA5AA89E8F163029ADD4A9209DE8A4F285766C06EA859639B92CCCDCA F59B1C2BB8D588CA754D1257BFF76B53984DF4937093AAEF79009D32A29A4C16 FB610C7D6713482C48D7F9E8410C0F00AD6E67021056B6035534E79F05D14EF2 4E8CD656294D05C463DFF88D61F8C38389CC0768F0DCE9FFD3767194816531D1 A9798D7102D4A227BE4770ECE0817769BD4EA82F3AD28B6F90A3945EC7A20FAA 526A3603C7F41FB8FBF219D323AF9278E1D8C65248A725755EDD25CB99EB7DBD 32426532D18B33CF06A0E6A8D3012634EFDEF645B2766D2DC922A9ABF5992362 B1C69C47FE439651B3FEBED7AC156B0FADC205D4028E6652D5C14F59D9A9DE10 B6D8E610023FB8029CD9C5A148845F067A865A78673D890F68622545D90F7DC1 744CD961E7DABC4A2EC118EB1B1189432EE9B637E0F811B87400F0434C0456FD 1DF9161B48A15E38E473D428F0F9C2B007B276DDBDF49C673109F94198F46433 1A0F62C56F6C7A255AE298A4E1D2741FAD5ECE08A7BB56325F36C7B142E5C77B 8763318B838066A3E1D88DBEF92E43941BBF29ADD57775F446FAB4DBBC43A1B8 82FD798FEADEBE94C38C903866704FD35B75F555A00A763D99F19527BF1BC957 4DC1B358ABE78CFBD3AD347BB7F6CA9CD69034BAB8D04AD06A233A6B3B479215 AAB8E93E541B845B2CE18EEDB47525AF88B9F8F65AD88441BF9F1BD09A2808C0 7EAAB810390949A446DA18EB7B1451C37C0AEAD75A502F75FF670658CF262279 9D4B992157847158D317E3C895C86F9DA1D652852FFE4F4E6D7AD8CDB00CFDCB 394070D424C15D2674EE7DEF9CC93E34C5328CE05B4EC0C0B991AF67BC8DE5DF 8068FEA2B6E0FE9A196AB54A94A4F3A9A12223727E30B9BDBE4569628ADE0A03 51BAC0C918311F7D4F74ED06FB4BBB6CF4C329B46C7FD9900E0D0A44FE9EA6D6 F9FC934023F31AE3443B0A6C67CB1A7277D2181C99C02E37CF340911C1C73AB2 ED1516E6AAEAE07B8FEB2AD8773074DE219D924A978127673B1D0AF2DB04C5E6 EB71A7E98FA45355176CF923E23399EFBA585A0468BA069DBB86AC7F08A959A7 38D4C3F61743AE92D6441B4DC1737B3C58C68D719EF07DFFF32101F661BEDC09 0827B5945478607462B91F7B5D53F6C5BFCD3D7CCA666D1F5F0EA0721232DD4C FE6CB293B4790B430A5E9F327E31F748F02B98493B0F26A8C40E271D645C45D2 6B056E1B4B00BD37F88B415C0D51D3C1D101FF1468B8FF628929EAC5F3087AED 8938806CAC6DF7177D31438291FBBA3E35623E030518DACA6A52EC0BD5A1F88F B3548A91C2247A8B3D5659E8AB404484A449E7C33DF288AB8091C14934C8F1E2 7536CAED4DFA42E82DF43D61DBE4C1BF6EC459DBD756FC124DAA9EEC70F8A333 1DD43AD61E52A77091B809557AF3238E645B60D7D03BD4E96CFB98089EF6AA1B 1897230E82B49E74F2A7F8628F23221EF97D2B08B3ABD26C0D4292679858C6C7 04D3F92634CC479B40DCEE9803EE689EB5D43A64E4AA712C4395CBF965B84147 C46D21F8480E61E08589A9755F1CDD25A15EF8E4B16A0EA22B5E37714A1D2140 0D093D00E21C729805ABFC6CACA45AE41CCDBF97CC19B1FBA15F00B0A44F1947 F91D8BAE0DF9A3574631662A484F3732B9EBB8C6D405A510B5EAEF9D697FAA71 BA070DF3962692BA55E15F0A0889EF4302E14AE25B60905911FA158493736962 7B2F0BE6F5F1AF28C036F78D6DF855DBFC2483B98C4F1F9B43274C1FB8FF7679 FD02EF09D5272AFECA7D18ABCD89070B82B9EC209399CF4EAD91F0B245E15642 9F59E007DD3D0C1FC900E37D408D3DD98298C0B19A51675877C6CE54FAD880B5 97DDCBF590A12841E0D25CEC87CBEE9B199E1C03F0C929CFDD3CA0317E67D096 F4025EAA98C92FDBF831E919E1E0F4198DED0AFC250EB930BBEC8502A298DE98 76160DF9D3E1EFBEC67AA1A92A537514D5A299BDEF4B1DE4881247F1177C022A D0422CE808A74A2BF2A737B683D4CC23A468C53FAE3F117B5B45E6CC45B80A29 25B2CA971705488A8216A0C7E50AB73AA5ACECFABFF89E4EB7C494E5123E6662 288C409D10804E8A87AD44E7456C95952D99BF44E7409F6AB1B3963145B924D8 C03EDFCFB3B791723722F12CE6E65C654270791E2A8C57E8B42156AC324AD626 0AAFC55BB82E74769D01212AB5D8E0DCAB6716440D96A015B006C3301694CD9A 511DBF8E8BBD82E08A7EA2E2C71D590693339EF71DEBA1624F805BB398DAE8D7 7C1054DDBD680C7812B3F7956769C40097B95C8244518211CB4E8CBD1B710F11 5C6B0F73001E665BF43EFF8F1EFE64ABD083EC0245AEB312170AC0698B0A36E2 50F6DAF8A297A61C113D8C1C414C84FE15A3504AEEFF5A058D4EA94C7C4703DE 480012A0BAD493DAC2FB977DAF090B902B07136905BDAA171714A5309FD20862 20361FE499E9A3A3C55306D30083306B05A31677B818403DC5E07D96BAF28CCF 01101EE6FEFAD3F2F623D0AD12271306FD1D317B88B6E08F40083739D2ADD0C3 C9D8C7402060DA817FCC66F6A93D79B3C551C8B55903EDF05CA9B6F88EF595B9 26645F8035FE7C7F3E45A50B3F702C21A36DB6018922DB451DAC399F8EC095BB 4742C55937D1504D75474B1BE86D741AFB76DC4DDE375FD2B498C07176005363 062E03868544B8152B2CA4A3DB48177BEA0453B1FF9E8CF6E173013788E957D9 96A2E8E5B7E3E6434E7967CE8959FF21785542B35C450A7447EF9813E0F40C23 731331CC5B5DC206D7A889BF28C25EE0B8B3B940EF661A7B7CB2496155949B46 3DD2B3C3A1B777D62015D2FE232391F0E726E7D9EC06B8FD8BBEFE7B53528676 425BE96E3618973D99DD704CB928EA1E6B5FAE0DCC178DAD591ABF2852AB2EAC EE1EFD849D33CA6A477F94749541ABD317BAC0DF5D00045B2F22D13538B1E20E 54F89A547BB95F4526B0A50A7FDD0A543B2DC27D294C1357C552230E39373C25 E15EE9E5074DF84EE1804C7BC625084BD09768A77E87C84C52C9DE8DA8165FF5 AD0354AFEA72597597803B3B72C37C6435E8AEE0A63D5FB367B947947C5E0914 15416AB7F77AE7BF786C4FD3EE90D096BF36B44F1324A34691770FA909C5D771 1322BD72E7D676E5F46EACF98513549FCE86A4A6F10E38FDBD7331A12DFB0067 B47436E8945826FA78F035C138A1534585FB53ADD19DF66DCD3D571CC0511AF0 64485CE812D886432BF82506E2E2464B6603151F2C3FFEE10E56BDA272B64216 5454E0F6CD207183339CE9EC239854BB3F2DFF9AF7E3B3CD1CED5E6F321CDEC5 E20016ED99F8938EB29DAD596414A9CE2D49D098BEA8700C6A24F19AA4775369 9E39AE99469915555CBE0A3A70E34EDAA354C9C53FC859A96C51F08F0641129D C674847611C5C8D75D7C25BB3303D3960F0C7DB214BA2CCDFA5563DF3FB76BE3 1E7E2FCAD50C10F97DA0D8ED72D7C343C703DA2A35D3463028ECD52221AA9D85 A3C1CCAF7ED3E365B1875C426D529D964F26F23B1CBBF09F2A018000091783C8 47634F8A76F994AB0DF851CED956784013043219167529460771CE55DA4C00CA D73BCEFB11B10EE261C6C975210A9CDE2A0D3B6BB07AC2158031383B03D957AF 94F802C12BFC375CCFDF92EA35930138652776E116DD646FDB8B90270769C60C FF574AF1549B37FC919B9815482F7F979B5B4812DC6D410CE64B0C0DC23A1942 B063503F32AA04CD56E57F95895DD3CF90A2A0557943F4EC87BC111C37151ABD 18244DC75F8D814A59541AF08E2BC003B66F8808625C8FFB4376F5D136BB116A D282443197D50B6B6751EA4E3AB22372971E7889D3F55536484EDDF8BC9CFA11 593EAD952E2DB8DC958BB5BD13F0E00C2B525D3BD9D328FB8784C0D63D29B904 B21B639D1A2B6C889174BBF95BBC0DDA8D58AFFAA0B65C7A95DB5BA5363232B0 B7CAB7CE3A2224EE428B0D8E20BA2BD1E657417B3412A6BEF61AA02F1857EBA4 C0620D289B131AF9B1606BA936D04D9158BC0A4D34E8C3674956E6D6CB88ED5E CF94288B2C60F65AD77E4F9DDE4C0102C17D20F566C244C5B98642C4C45E0C92 D60170AC6A27ECE74DB6DB8CA51C65FBF5DDE636256E49B73E17C9216BC492A4 A09116A84030886FA49BFB8D0266E13F54CDDC9C44B8F253987FA3E3B64DF5D8 631908713FF590D120EDFC225E9E616F6107E5FE5BC9615F0BC48E61D0D6158E AC7ECE46381D77AFDFEBB80C7BE4EAFCD9C5BD0EF9E7C140F61EF38470F37AA4 8FC610991AD37673F880F23A15A5E2411D5CF0729AE76240686E4C23FF131837 4B386EFB31210E3E8557A887DB02AFB07C288C85B2BE2C69C7749A2004101E05 AA5C85842928A9F5B3E5DA07F88C84D7CF0A8870A5A31950127AC500529F070E 2A2E08ACA022EB8588C94455C8ECF2355E8D20CAC3EBB361EFB30ABB2C4B9B33 44618E97DD1841FCEA7D0B26CAE9E284D8B420E5B8B3CB2B6240B8DA14400A1A 41CA23ED1BE31BFABD2701DD1C761FE2AF3DF54BCD2957E0699F7DDD06EE3EE2 A4740C9039F96C5064A0A2B181AF0CCBD932A4B1DD0A40318DE4C5B06CACD064 6E7992DBB93C468A99C78835A3B15CF5756FB754E4783338D987EAA3AEB8AE18 765572C559124FA00796E996E8183A562D0FC77E73E7852E544F911B32E6F26C CD622389ED5DE4749B912A9D2DB0399D4CBE04E97C14C60E4C480F49E0857B1E 987B3D643844FA04AD02F81381F8FB92EABA475917EC7F5F3A5684177FE011C1 270F4A444A4B9F8D041E6A10EAC655D853CF35950A068ADC8BB0ABD9A18A4099 709859EA0730A49DDEBCA9E97D9F6D0E7994B08F8C128A0AD0C7DC60524FC160 9C4B75C7415870156EB74FDD7AAC103A4FECA7B50D3023402F7EA3701F003FBA A66091AFABB3B1008DF827F6F675D214ABDF8C2054ABA8BF405E5EEDF580DC9A C696BA68617557D12D6DC367B5FC819E7A4E951774850423E350934424E20BDA 51BC1C51A1536346068179D14FB75B651107D116E1FDB83CCEED2432B3ECA959 35DC2CF3AADCCE812450644450E78F63C0BA8BB2805BA1B79AD99246CCFE932E 30A624A4F957C4B08C95EED5FEE22D0E525B1E6E1F87F6D8A31A73ECF79B58B7 02DAE630C5CE4322AE12798BC355EBCE24B44808B249351308EAEAC2EE98E333 383B9A1D56A80D435E72244B7B855E4EF779489DC3F4E7E4666B4DC9B4CD9931 C77C05139B294D54E13CA10CDC27A13637ACFCB81076324C4975CE14C4AA81B4 886493C773FC047790424D411A46C1E3AD219A64BB91FBFD064ABE8DD9DE2D51 0543215C5B89CAF05DC29D4A6423EEE2C3E5F3793CC4003FBF8B54A1969A78ED C61E35A1F477015DC696F5A66DDE61DE223F6C1CD244EF27D736E8D31DC2BF0B 27FC95CD5CA04C6C3EA6434F76BF3E599FCEE72514D00586994C37A63F328D07 7A0034190D75230A10EE0E8A835E2BF1230794BD32FF48A95F7FF004AA1AFC2B 59203363FADC5D4A353EE04BC611F9935A0950BC821852420B82AA187CE361FB AC0B6A30B54DE74566A5F8622C10A6B0173F2F308217592DA2788BE4515BBF9E EC4207994168E3B2853C9C2C0054FC04AE258996B71D4353BA14F1C705137649 42A1BED1A4BCA9BAABCA6DD1E0D7EA3BC08AECC6CEC517CDC40F862A63AE5251 78DE27667835242F7C8299B6B1F613436192445121BEB39E195D6967E4185DA1 459004FD09593F8D052D7F09B868E7B1F464140AEBCEDC806BB06E2BAF294F10 41192F02D791191863BAE0358AA72403F398D00A41E01AF6119FFCF1799F0E63 037ABF5CA1B0E34F67AD168A3D6BECC6293BEEBA24E9B731FFE22E680435C5E4 E4296CAB1C06B8F32786F98EF0C4CAC6957BC4FBAE6DBEC7A792662BEDDE3C71 A1C11E726DCF53C761C5382A165E3F45C7C4CD7C5569B8E623B93ACAEEA069E3 85FAB9301C5FB2E6E5BA71391BEA43FA232F82B23548FE2249BE27395F2EB2A1 4DA40486439A0E8F412CC692B79D2CA10DE9DAAE77BBC33A4EBE934F4ADAC580 0F511CFA1BF6405DF5108AE3D5561B8DB4422A2CE1A7562B66B72ED7810ED84D 0C490B713D28F6EC8C94F686BC95E60B432C4C36F9C48C439A9E54AB5E70764B F981E70D042AB78596E6BCE65D9D574A6FE55FE8DC1B537A0137CC28D856E1F1 E98B3A3AE810A3BB27F82BD4B2314B49E0D19D0CCE505D2B8824E9AF67592DB0 C358977DC2B62E14F9283EA3B358825D0EE95B4C7E181CBA53DA16DCEB2A1BF4 DFEA2BD181AD50F9998FB029E4325E229B6CD872A02194B4EAACC9D4863F3654 8D44AE526E8975A93351D8EB516F05790A542D82FB390D6061DB64EA3F92FA33 0CA03ED252D79E268FC074B428CB7D52A6212D71B7FB92ED6DDBDF7329FB2FB7 BC53258541854C3BB53667703ADEF948BDC781E275BCF51E675EA3CA6A63D37E E3A3535921CD8BFC90DABDD682CBA75B59717013FF65F18B057FD5408BF8EDBC 9FA0757626BF791F27FDE82EBB794A180E421DA4D73E17214FF131B491C00482 B618835BBF15EFA28B7260E2E4ADD5CE8F3854E18F909892793B1071636EBC6E 70E5D314740321CFE660203398248D1378A969A5F63116C81FF3FFAE559BD17E B344B0C86B0FCD5705488C6CBA392229476354794504729ED3D0998A196A7A5F 2D9E32FE5EA492B92324054F12FD25FE62095271C63610890810B064F0D3A9D0 4C85E87A6CF20022F3D350E0630FAB15C11927173BCCC4769E8EEBBE19EC9289 E66B4605130F28DC7A3A30F42C40A2958D0B15B5F454F5D2B6122BF764C9AC36 2E15300C03039BFC361FADC9400181153FFE95E3E10FE01CDAFA77CDB1FE71C6 778327C8E16DF0E56A803A8C83349AAB23711AC63ABEBBCDFD088ECD5B53A767 C9CFCB4D2E70D155D81CF6D63327DFBA9BCF8D6E48A4B2D23BCF56A264E06937 36FD141D67FC373F51F5E7DEC7DE00AE64BF2081A08431160EBD7CA4DDE3F0A3 616C67C8931F475CB5CE7BB0CEF0747388DD60094065DD68C7CD39D71CA11802 C02C7DDF6B4EE63226D1E7257EC8F0930282D1B63C1FA1B61B6430798BC3C2E3 A42B847096C5100E2F5ADB3DD0C2EB66362B791171BCF4EB6BF881412674D26C 0EDEA8FAD11DA4FE0F437C06BBBC51D996D50AFF7E4DB8A68580C738F16ADF42 D0AA97BD4AD60147AF5132E50C7CDDF157F3EEA924C604F3982DB60CABD6C05B DBBBAF8C2A106155A4333C47E47E6DA26650F27B7AB6ACFF0BB1CF2D19D33581 161FCB9C327869F5BF458D5D72F052C019EACE9E81B8CB804D3E98DDBDD84731 A2F10A6C185EB88AAEBB9ADF8C6D59FA3D9EEB8933D7318FE803118A3FF313F9 9E5C6B9BC40B731529C4FDE143E011DB994010E2C67327DBA43EA46BFD2A635C B2EE4F450BB5F351ACC92B9844BB598B2B5C7AA97E854ED166DABF8D9102A1D9 CEE2E849E38B5E3976209FE0D20B85E43C3BB711A08EFF53EDBD6FD5CD9A7CC0 82E026338FCF1760683192D2D529FB70A3FCCF6C5A49D798751AB8319803B62D 6338515105D3FDB88EA2D55D98528549CD41E5E68BC84342C7DC74E87B0EBA47 2A11794A3DB0FF8E3E0BA27CB8F5DC6C5C0DF9E02EBA8B58ED261537EEB31B5E DA9E0440F7C86461593510C8887DCC6715FCFD5123F24ED2E9C993C4FA7EAA55 30F4B9667E704D1A70CE5D4F9B105AA4DE8599B29590DF29BFC18D668ED13114 6BC12AF3984964D8832BAD5427D4C255075B5547D3E3FCE9F1B89F974AE3DE76 D4D5E64A1C0814A1C4E8044F915EE5AD2DFFA33D74297CE68AAE4F1A2F49A7B7 EC76C0F376543A2C71F40A758082352A57145877BA5E50E5993CDB3455FE0270 81BC76CD6EA6F27AD8366DCB93095F9970984C5C998955D211CEEE355E793164 92209351306B2C9A320B435805BC78AFE034CCB72F63439A5EEA5D088D48B6C1 3AA1BD260924912483DCF5CDF5D6644A437EFCBA5CF7A95F1A27354AEC221D6E ABF678B174B8C5530619B2CBC5F510834BAFA97CFF9B9D8135413690FA3A5F56 DC60B0A6079251703E1AAA088E5884AA95CB08E7C7FA1228144E55063E0F8332 C0BF3A99028FC4BDB137E87B7D0018392F89C6EC96DFCA9440823FC5BCF79AB7 C262A1883F7E29CC5E7E32E7BE0FED2E5910F9B4FF0E84512AD59E40D6056FB2 38B2B63E39BD6065C0561C3133CA28219F0B09ACF3D8E036FD6CFA205C30290F 9B4022AD5441727C7B99D5694941D9952ECED415A9D8E550E7EE96A7E0D768F8 A7A2D2DC577C237D065D555CDE834A42C5DF55FCDB3C376A553AAFBFA0519A5A 59FF03983F190A05F8AF369C37002C2119F3692FD0E815B668EC67F6303E8F8B DDA3779625C7FD948D85D73705103FC10D315BB062CB25B3847259617963A35E AEC74F7DE3856FD4D2C8C499C0CB6F377C75D04087AC0E2BDA98E983E956EC4A 43537D190C8DD13741D317FB7AB3A0F80A1614B64E039611A6891F58B9E4A6D2 3CF13B52E86BC0F351007A6B650A113664E1B140F4029A0264E50755DDF0C695 D9111288860BA76F4BC926DBAF97725E8B801BF24EAB68B7643C1AAF1C1BF261 0F5E35A21BAF33D0FF0EF7EEB2300EE7D54CD3509B4384D4214CD0CA43C47722 60E310785E9EDDFA0FFFA579E053029BC42A8C186F6E34DA59AF79EB46AF277A D81CA45EA54D36421169F7A211356D24442301835209F3C6053AE6431F385695 264D3F1936EDCC8F9A0169C1A7054D43E625A6F781599A85DC55BCC9827F56AD 3A102729CC917768C638FB3975C8528C3918BC8447D454A9FAA48A8AE68EF098 6320534B3BB40984DE28C12DB1B1F81F04851256D8E25DE075D370E18728B0D9 8C4B6E619E47FC072D0526A40ECB2DF4C0E6F37F59DE4794F95F1FCCDDBFE954 6E94CA20E5430A809A9A59E7704325A02EADF642F2FD113679F98213C0356327 4A14DB5B96C4B37090E73075A5F33E2EA281A4D86D038158AF9EE6576074EA8D 856CEEDF0C5D5263EBBCE4E59CC1664C6BDD87627F5426A3695D64F119145B24 8C1A766A8918EDD77DFFBB45321B9F7A3AD17D7D548EC86922C7455FE0E08244 16F5BC7EDBA7BD39E83E35F188877B90A3304D28EE804013E9F39C0FEA51E41F 86908A275038A0B9042ABE0CEE2BDA5D99A3C7534E5917CE545C1454093A3E64 9CA47D88C736BCEB034D6E2B6BBAA9950D0B289C0B96BBDBAD146D215BDC3C02 675743A132754E33AE73FAD1A471570DB58EA22FF992AFADBB54B73365C15ABB CFF9E2E772B9D795B691FE8452147290A4B85329A7C5C18174ED5208C099FB78 CF7162C4A624D70EA13BF9E044D4598082C0DE51E3D33DCBA1FF0D830031F1DB 1D758A64B6CF59D252BC952CCDD0C76AF2BA481877B0C18334CA6F62698DAA43 6A277AA409FD734DC0F0C57F66D556E60B376C253539B91BAB1345F752DAFA2D 5B5FEA338CE0B339B349D4BA78C3EE20C8440D847DAFD6C04742E657D8338CF5 03EB09C84A95D91D488862DFB936308A468D193C0495A96F1FB601E4D5BC706B 758CD9B2FE15D59129189CC50724ED00B289A7DFC7BD480301FFEDA3EF3A799E 01DA626023E22B2BCB6E3DF931E43C8FBCD979FB104F69805288988034FCFAC2 2464F2451F08E1AE5F01FEDF647DF3EAFC15527B5D0E73B5408A451656C3DE0F 00483321ACDEE71919B579F8545811067FA99415B919C3DF15FBF557DBCD61C2 B256A3FE727FBF06474869DC4B5240A514C88D98B13A3C53E9169B5400742DE7 72915BA76F80F6DCBEEEFCD72F92A60FC33957650BBFA88F4F5F1B24EC61191E 7800436A0EE67BFC7570F3E2F04433C001454A7363B7463CF291B7AF26B3023C 9A3DC990CF4294B45E40589D74908FF758FCE539AC5D41E1D906DBC2A6987C7B CD44ABB26C9BC927D51CCA5EC2065FD046E1968082ABE5AE3CE3FA9873AF554E EE694ECB7E4AAD09893D559EEC7BA8165A4B2A62725FAF69E24F17809C2DEE15 C8532D5FDC78FA198A3F1715991F701DC72952CB0D1674DD8D5CA869B89D13B0 1E9702CDFA1962B595C2E78BC88427C303111EBC69DE9239896BB232109D058D 46B3E63ECAB3FA0155D9AEFE460455611BEEB361A05A5F5AF5CEF67975EBDEDE 02653B0547ED20DA2318B62114855E50AFFA5D243CCA72BAD93AD287D41DAB74 267BA3993113161957446C186633DEA99DC48F4466BEB2F87AE622037CF253E8 7AAEF308D2A29BDBD2F30C3B1CD6BD1933CAB45BF371013EC70440B71135319F 7B87F79AF9E6146B0E2E20AA5DB4F1D1278955B81C34466DDC0FCFA82881DF64 37B5B5730C23841FA8D2D9DBC7FB0BF35C599957461910E06D65A9BE8382C088 6C2EA2C4E68E719E96CDDF3FE69673E7E0DA5C961ACFBB8C5B59ED70B3F564B6 880E4891D65E8323B697A479D4D69AFD8AC64FFF4855AD6581F14233E07FFB85 C43865CE72EBA45DE70115AAA09DC0DA926FD9844E3FACD82DF2D9E312A2D00D 8089414464217C6E3D5224793F7052631BD39A57EF2E7E5E97F830FF877B9E47 5D1B841E6140F2AE1EF7FD4CB51A9F7023E608BECF089419B43AA2FA159AA0B4 5BC9FB7F4804C2F2123BF6EFE7864C00B0BDE5D9B0C3113184577024023D0874 DD2357BDEC1F2FAFA0AC5AECE52A84417C2A0CB8413AA2B5F4C198C88940D15E A4E059F210D7A9E81CBE5442E38BBDB53F34BF00661A9789DCE2E760D7188C17 7304993EB3A648BC22333CA1C75CF0FF4A203D6B39EDECAAA11882686D41B404 665F4A0F88048360CDCD1A56D89083E9A71394B4BFC756364B24C1E53472ADE1 F108CD430EFE084DA83CC094011F4AE440CAC622250F47032C3052124930D01F 5454E8EE57168DC461D51DC690C4A8F6F6B1E697C1B397910EE03CE2BAAE0ECF 52F0E7F608A00F6BC99693A27FFE9039E3C4DE5CBEABB7EA6474F809EAE77080 C85F923AF04F67B7796B5E04F1E53C6637705A3E153632263DCBA0C199947D99 4FCD4C77448D1A25657A094D67961FCABEF2D0AD66748E2B00B330D6B42D2455 5DBF54658695F59B77C88CBE318B2217E140ED0B3DD8E3D38C61D0B8B36E715A 0C15AD612A127F738E8F783A47E67F664DC451C8A9DCD5928692DBDB77F5D1A8 E1E126EF0A626D7579AC7C7F8029F2737EB917690D20F43AB99F13E8ABB62D7B C158C3B8544C07381E837D6E62EF26902122527DF1540E4CEDF70B5CB8B5556E CDE64D02C7DA907C08195253426D89E0E680630C941D4465D9C9F1EF4BDDB10F 2061D8FB7A7941FE85F3B90A41DC64B3D31699C927CCB1EF342773D39976FC99 27A7179248498FB887D8CE18312AE210D5AC1F73C0BA17E4B072DB1C67275EA1 5CC592E5FF44961F1A877737089E64675E5FF8FFAE5C19778E679698A9636DC9 30F7994BF7B09BAD35AB1E8FD70553D3AF47674459DA96338C49DB2A617BB8AE 484D49F91B50641230B0493459C19F4A16CF6B844943D3F955557A9455596124 9F06B521443123197F03B65D0E97DA6531948293A5A37B1200E84C98BCF737AB DB4197D760D3FBD11624E3EA5A9EE506451DE670B60E80CC018E9F693585050C B0CA46C8DD9A1BB66E87B3454BCFD63F262775E7B77E452B0986A06D552DB817 83FD2BBA57381B8857AF54491A517DF868FBBE341A7921113BA246393BA35B02 E7CE355E9E5EE2A3B86502434BDFD7B11EFA5FDA71AD6FA82F9DB96839CABA40 641735643D3D8BAB525DBBA70FCB14BF32FD243AEC192FE8AE5306757FDDA615 2335D4026D67F16365F3956C5AA16361BEFDD321A23723A19183BC48617C0E91 22CA884C118CA164AC4C69BDE4D355053EED86E1EE402AC267975DE335AF5829 1B9670CB940318D5E4D280ACFA707C1B2DB714B5D4B240BC05FFDA01BA8E27F2 5A7C5058ADB99A9A34479A8EFCD5440514E58F7888A86F2EE1A5CA50EDFF3DD3 46B0D11EFAB048328529FD1B4338DEA3BD3D3F972B874EFF8C5CFB13F51CAAAE C94989B364E8ECD3D24FCCE6181B355FF5E18517CA97292A33D89F658DA1466C 8DA6D89190047C95ED0929A236CD4AFA47029A733579BC915B1823BD5FFCE1C8 00C81A685EEB4BACB0DAB244A84C009ADE296E5255853B04378049DFA06E27D2 FEE3907089DC970FE0F4125911FC22E1A78BC522B27BBA4E4DEBC13E96CCA637 F3827B17F47E0B683B6DAB16ED128BDCC092BCFBB3106EB6E82724E7B5CE5C09 0EC946FD8D0005C33DBD86746178B1559964D562A38CF784194F6C40739EC699 DF41E09ADF203645A0A72C0274064EFAD152CD08F4C4944F5C692B712FB0F22D 74C94D07B76B36904FF857DBC3AC1B8E460A65A27BF6E833ADEEB7CDA822D369 594E037CFED54C5716F6DAC2160756D187D8A856977EF03E00628BEEDDF781D6 A5FE5D1DC12C7FD25AC2EA940F6E7EB1CCBA238D437B0034DF739B11BB083990 EB83C0AFC7F714F52E8050CFDFFB80518E47B6CEC8511E2D699CE8BB9011F516 C1F9EED00A99D40FBA341EA0DACFF4FCA6FD9B4EFBA156781D900FFD9C7413FE B1991AA4AD68B8D13DFB39E410EDE8F7C53E10260EC749794E6E5F83A8967655 B0B315C1EAD09105D3917F8C5DFE14C7393E68AF4755732C140B49A8A84601AD 4191E67EA75E57C05EA6295D451ABA6676AF6BA89593BFF0B3A1B3684E9E2A5A E7E88BFC34C60339C732A27F0B0851AE2B75E70FAD12EC0D6D32B46951373CDB E13FF289375CFAA534215D88939BAED331A0DB7D2B45272929361AF926810674 BA5D358BFF2A8052D228575D93507B0D4C418F3AFEE3893D024ACC3A7BE1E909 788FF2EA30F9DB4F89970F9863632ACC9CC4587173EFDD5CAB6F8BCED73BF0E3 ECDEBD752D7B80F55DFCF6DCF5B1A2903E3F0F1C974367F7C32C406D6321D48F 565363A217B06D49F6CFB22C48EA8D59E202F5A65FF98805527007DC346D6084 DE5711FB666C8540990DF070C2EFA8A4BAFFAB615566D68C47F554F0917CC795 1822AB32CF304C4C948D3735EE23F013AE70F80C04F8BD6893EB5E2FD9892A63 368C3418B00E3B03BE1C5416579BE75A6770BF5D0AE0A711CD0FD53D4A4161BE D86ED6C54563807D1F00C7ADF3867CF998BD0602484524925A1C27789C30C321 9C09F04E4D52781EF29D49EE0CB7C981E897E98F1B97758D3E74B5313126DB69 E97AE7AD6E82460EB5B1C5ADFB5970A956E94E62B10AC502BE77112C5AB7456C 47A4F69052E1A93A442BDEC3631137DA903C9D82C1998C1D5247D125A5831610 DA04A2A9A0A6982CA1E1C3BE629C8510477F499F8A2759A548A89B82562B9D43 1CB045AB7220975FA3ED7A6020E45501573BB60D3A7D70A27AEC016CE381ED9B 20F4101A870E7ADF0FCD31ADFE5A0B078FE0BEB19585B8B69C36807BCE1CDD69 30F7F63C2C46CF1C2680E5238B108E9EF9C49436B30F1B65F54380DE1A054ED6 9B65865E84499EB92368C1E7A9AFC8ABFA90CEB1E23F044E128EB0BB6320D8A7 D6EB13B14DCE472819CF68D1562FF6EB4C381768300F5BD4E6CE0A69819CAC56 3DD00F41321FF1F724FAA4A3436AE4FC2C82A5887FC9B2734A6D03076C8A2477 F68A20F492FE7D1F56251787F3382EF18FE71B912425A8E23A31A52C12C9FED3 F5C25F1B3EACA1E25F1D04CDBE17C67A60945A7486ECCF8F233B84F8A2A26FBB 857D30F01A64FBE85E251A9057FEA16BFDB06DA13C0E8A1A968CC52B78C94F17 394EB5090656FDB658DCF6DF36149E146C41FE01F2CA0CBBFBB619BC0898FE65 9B31C61274489EF25D68C03CC6B5ADFB27DAD833205AC683D16E103AF57EA295 32070EA212E82C5E6DDD56119A1D1B7DA0B547BDD304077C523340CD8C079AD8 C328C9615096AD17884D03B2738533D1507808BE98388FABE8A273658C9265B7 BEF0EAA8C3F14FD9AACD2747A3D6260DA6826E35DD22C9E9E84DE2D8BE2DB66E E043EE306DB65BD108A764FA64510B155C2C8439D08FBE94E8726270B0374D2E 750FEFC0836E3F20C930E879E8ED559E4D03CC82DDBCFECC8B736638C90255B9 9DF3D22938CF9E5E45BCDDBAB6FAC0A7BF5C37FF29002ED2FCF274EFB5283A1E 587C62782D23072F2667A008DBCD3AC32890FEE534BD98FA18309358ECB359BB 01AEF9CA51EECB2FB45AD1C508F2CBD0B09C989401E20EFA6C013987D41E4819 F6BB1D53464B4A293568A4397850E705D2FDC3D04B9405425EE149B9F14A891F 6DA68F5D48152B47EAD8CA5EA7D9200593A936999154351219B59F7AAC62A6BF C0692670C084DDDB84A2E9D26BFFA4BCE7E83894475187AD9A5C727F38702854 F6A7BEF5950749D389DBE11418426EA2551F0EDB8F08F863F4B6362966A025A6 AE60627682619A4E0AB4F107873BC95629153CEEBE80BBFA6EA88D199E4E1933 57D6E0988BE6CF43823DFF0266FEBDC140F50B4C1692CBA565716920C50F1CBB 915BC0AE6D2526EFF6798E355F6CBFD5E662109A56BB9D1E24100032043F6F95 C1C043129768414F3350CEEDF8351EE52265BA2362988A783593B45F5934CCAA 3EA6F43B72223BBADC9DCCFB96C72442AFAB9CABEDE358D69248C115D5E8782B 705C85EED02A93A62D9E5A4420267ECEFDC6E038C273FDF628C624EC699F7CBC 695CCE0A9929E5F865488056E52B71DB687B456A01C5461377B64A59B705610C B2B07ACF086B6624FFE562CFB2CDAE2F971FDCA8FFA3788A9D07F03C32FAF133 55EB5C068F83144553B846A8AF2C96D233C7165B48BB5A86713E2A13610F7923 0936F0FE514488E74404A6D8E68AD854779A94F438FD0FEE1B71E90A16295810 97323C1F6FD65A3E1C7F1B2ED0C8823F3B60343C33E2E721B6B1F6B7F907F87A 3B0D83943D284A24735C0E7EBB15E51565B7156C9B9732E40349506F7C50A2C1 AE0576712D56B4DC424AF411B8FC8D22E51D9ED97CE7DFFC91C1686D9AF12E4E 43585E8F608F1E28EA0D8380071370B5A197D5CDA7519795CF8BEBCDA87A2898 F98BE3070BC78C8783CA6B86BD319C74534527939BC74632E0BED1D307A8891C 70024E5CACA084D5D360351BFB19FC95CCC1DFC4139B64A4CBCEF14736B8F46C AFE2D073E7DA1FAE098C10F66A1960CDED656A93AB5746EA2B6F3170C6765F8A 4200DFF78618DB5704C0CCAC9756B43DBC83ECCA82E0CDAD8F02C697CB6A7433 54FB7C8EC237F0BED4FFE75E1E7B4AB6501B7A68A1739A3BC734D5CF672D0E5E AECE7EB9843572CCDA1BD41530D2C801A83811A983061C90DDD3C229DF29DAC7 995D676C2F316DE1BCD469573482601C43C45797B822546CAADC2029507098CF 6E6BEC36308E4B67D8FA04A75591807159B60813B77638F73E262A9E479DF1E1 173F9B8BE5E88C5DCB74CF6E7D016D0B4570E98FF56BB9FA751CCBA86F187D79 0938E136FD63A39A7F63EFCEDD13989F6A3D460BFD26AC910305A69FEA59E05E 8E2AF858FAA20D8F2FEE7C491549B9064824EE1B294A6D1EF488964C369C60E3 B24BC55774656069121DF30C36B85082C89A063D20F84E9B0240F34197960A42 1CBE6677230342B3534DE076C428E0F85C37A6DFB0CDB826BC4CA39AD98A178A AE66311F2F13581E7A505D702AA8A441DE1FE5B9A4D7E12C0DC98062069FE12F 5969CCBE00B4A5B63D531528EF5824367384DA5FD611E3CE3D1A57AD841A7AA1 16F86F45E79F4CD3CD9D6AAFBEBDA9C94A1277785076B7A7DDDAD604A9F2A34D 3CED4C9AA2C16C844F2101C0946A1ED2229A928FE5CFF54AC42C81EF9621DFB8 AC9F428FB0ED00BE2D98BCBF228FAFC5504AF7E1F2528D48A179C217F22B256D A72DEAAD3C5035A20D6A1EFBB5C81AC52C491778C635AE6FB12AD13184081D73 20861B0A84006A32AA7D7940B259711DCB246A8D7C99616937374F8F50A9011C 0DB65480886BA0F03F5828922FD5DAAF782AC799B8F42CD66747E2E44320D93B D00779C79A89A73112788D963FB79F4191BEAF949DF8B7B6214123CEC4B8517E 6245034E9E5A49208C7A51193FD79140A899FB3B8B9577A82A609F29A880B9D7 3793D6212391BA19F3D7E0E8F83197504D1F2EA916F009E3D7041C9D2FE453B2 19A1061DC3D8EE63F71BE69472B35EAFDAE4AFFF056EFEA6ABCF790D520AE380 B5ED1D4B47567834B0517FEB363A039D908EC84F44510952ABF6B636A6FBF9AF 1E927EC78725116FEB3E51080048105493088F1F1169E01C4C9EE313CE36B00E B408538C3426494735DEEBDD796F85C4BED7488A162B926C679E10F2B2F0C915 66DCE8EE446B4327C19AA9D8065E7C21A0DCC4CFC3868595872C389624043900 0553ED11F936C055BD3C2C6821A9766AF12649B6DEDF807889141D2FBE9CC357 031FDE462E3165F8CAD4337BBBFB0E77F36D861C601A2C8CA58DCF51378B0C00 8969ECCD247F77C562209555FA26C4C9E1F7F8CF6C2D7D62EFFF18C08269D23A 0976F5B10E0F16261E58C17B9E78A79C6640C7AC370B3C945F6A9DCC8B5B3683 6EE3634FA96FDF043515C92C379A633FABB014E158CF5411796F919155465E5B F04EB8E0D14C41A548A57924B0B2294F03189EE74E4070F637E4E9C2DB393A8B ABDEB827AF56E01FFFE9D937757C2A9AC34AAAB8EA7910679B5CA0B26903C643 820DFD41EE0626E32599C62D1D9BDA124785D23138078F5F5DFAE2C7B3BB304F 88C7C2FFEF7E5CD3002296A3D4D6EE19ADC0C83AE70925B4BBC60C1CF60C361A 9C1CDB202B4154672951806DFDD274E989BD091BFA3A17BAABDFDEA4D9B7865E 1F984420CDE3B7DD6470D3368744375D6FC9490E3F0AD0D7708B54B5CB2A78B3 F92A504E568A87D301EA65DFD7EA79F760DFECBEF1ED49FF36DC74C5DCD5EF59 61EB26F3809F8A8C4845F2030FB6E210E073D692D3538567ECC087BFD29DE9B0 600898FC4E6C446F80AABF10EF3CCA585852682546DCF7B5B64DBFBB9A867DA9 EBE593D5FB5CB67B63DBCF5C1A8AF3389CBA3CFCA84DB76FCE8484A4D361B1DC 36373871EAFB139A455C3D2E69128158B139727ABA396B9D84E8C6C31EACE4A3 F27DA4D64ABB59D60957D06B626FB6402B3C7A2B9811C0D4133ED9DB14365BA6 9298504FB9BE097B1AB397DC21C0970C2440BF9093B5A67105D5DA24986F6C78 A22039F9DD4A537E29B421D8A4337C8B0826265814CCFA5F2B43FFF8ACC9A510 6F5A24F883C69AE14F883FE0E85E0B4D5908BCC8AC214FBB6AF378B05B7B17F9 7AD01899C02BD82DB920ED1299C08ECC3F08DC5C500A6A2BEDF0D572BB569D55 0ACC40A4D26804286DEE18FA635C1C48DFA0C86B236428FC41D902DE5259BA8B 448DFBF3E691A477AFD6DB39B5CBD7CE771CD75972F772E4967E6DDA20B5BD31 6DB3B1A40F09E5718ECE4C8C9E44F695E367D97A3A95326DA4558E7118A83852 1A506D7AE6EA8D3A36D4BB952D69DB7DCC591C8DADABA0CB0BFFD457B6123242 041F52B4FAA7FD59CAE331548A967AF4A8F417BDD82DABB26972393B8F059D2A 3D082826AA168A9DB859D0D52D8A02A1AD6662FB033B6D5E5BF21A3964DD31CE F324C24C06AFC86F79BB84508C0A54E4D5665476B430E03E7C51B480BA93F59D 45B97F4DF1C4DC520307A39196556C95E0730B93F747C4AE15221ED403AF6F21 E2509A3A6A7673532B25C1C2A0C73C5B41B86DDA8AB4B20189C1194FF1E37E98 B43A5BD5EE48C676353230F8670E5C4096646C78399E0C9FFC67987226F364BE 5EB1526ED20FCE2B71B8EBACAEED8518775E20CE0E4402EF57A738518FB05F9A 06D7840D01DCB93034B5B47F785316F45FCA7EF1F016B4A7D753305DF7D44C7C 2859BB73361C5D487728F3382DC4B99CE3F703BC28296BF578238F4B8C1D1019 FB3C44CF35D64959DD4B2BD45C6920B352FF492BAE99AFBB09D106C935FB76BD 773FABCA22D9C0044F8680AF929FE70DC38EEF3E0A920E1F663FF631E82257E9 DF1CB4CBBA73E5B71C476224CFB957D518A637CF1778CA3BC5021D2CC6197580 5495F74C0B47106391C3E8A5244D7658BD7801B44431D1B4283B6377CD89FD2A F80871122FA615F5676C8118D9135032B7AF9D20D7E9EDE7B98AC98E301499D5 F741CF573FCA46AE545F167D3776248F6F80860ED7CC32350A643E4EAD93EBD4 7AFE3354F5E3228ED710C58F282E7B96AEAAAEBA2532BBD29EC1676C236D5BBB 9AABE8030DC575E84A252CD27C3BFBB7D7B38B4B56C5D1A300AE4CE17418C411 00E9FD1658DE2CE49E0B844843ED520CB7117AE965B1419A36E405EA8A106C73 B00186A9FB198E8261782EC99DBC47BE6059D7A2960C3661CB6780E32A6CCC9C 05CE7CF1FE71B9D00D65C36123A2A585295598472E3001C4F133AA97BA99DD39 2FC57FBAF515D67EB19F924A52990B7481F4E0D2F8BEEC6E9EB499C90465D278 37EE198ECA569277DEA1B825482385EA6E4C8D54E1F16D5507673028DA1BD5DF 66EE5DEB21ACE0E39734D1C3EA560B85B7756BD57B45DE5EC6EF8CD7AFA615ED 6213FD951B697B2C11DAA3516B9D6B275D1A4A9F816ACA5ACB5DC742C41CA9C6 1754BFE8D3339312182AFD8FB06CB08500A176452B8E9AB5395BD37445DA325E 550A977721FC7E79FFA3CC8A18EBC17B0180D0ACC60A4068F96ED87CEEDDB92B BE3EB2B85F93A1E7A6EB987F9CC58CBFB0942FEB598E0D47FCC744A6010C7E8A 1A1C03924402FDD03C0460066A15DED2800BD59D620741D3EA2861750F17DF99 D965403110DF3B631F5BAD22BA29D33DC5C189EB06C5088329C4593D9B3EA1B6 385944A29DD7AE9507B464BA62F93EC42B9B511E8FA06196239BC5ECBB6C0ACB C36A82B7F9836215F8302C114AB7CDFC910A55B228B827EC10E2047ADCB48027 38BFE21ACD1079EF1BB3F5500EC2F3457E5C72B574BAC37C07EAE589B031B76E 44C129BC3175101A067C2F7E6EFFF7E0D6DE753D33DC95454E559F95DADA0EE9 E3DD2262490A42B468588F3671279024C58D0C82F93E253A6BA500B849B8938D DA00502EA37E3D1C5441C1486484C2CB185CDD18CC60758CED663AB589D5EF24 4AD698B8D089696E84114F174819C5F3D6D2F925DB774ECD56A66763ED17E874 CBADDA5EDE12D2F139A60B7CD10067AC931E238A98DD6DDE689F244C7CAB170A FC96A25FE1F156D70661466D797F705DF1656E207A352A75B78327D35ED6D4B3 F176A91866D3292D8D595B51A32F06F0EB3C8878A2230129556FD9F0C31D3F13 573CDF92AC766188908B73506B0507FE3C8DDED3B9CDD816ABE79730F6C9B7B2 7E503B8F7C0A2AFF0BAA2D8C3EAEC2A965ED3470CFC6D53C3B3F577476ACDD79 5F996BC0B78701C477099F325B1107BD88722C281549719FC90F6E86FFA651DB F1AB3F803A7180177449BB9C1C27C10DE9342DAB0D171E5EE301827D96443ADD 15AD40C40807266549EB97A8078E7150FCAC8BB9DFDE2EB9C103B8349C560B3F 904A52443CCE4C46881337E79E8D83B4891B9F569F715A8117E6C5BB1EE90A1F 396BA1029E3D21053A87AE76AFBCF5C170374D45507B583F1C99697DAFF6AA15 13C1A2E0F4A367351393EC55E6A500B02F47026B7698E9BE0A067E5CBDF6B7E1 5A72E1AC7ECB04071E2CBF6C977C2021B7644B210D368B75B87227D900A59DDC 8512FD9646262A5C9D090BBEF741CAB0CE9E9ADC7793C1BBABFE67A48E818D69 1814E92D1758D1785A1587AF1C6068A48BADDE1E8DCA068CD1FFED1DCB348102 ACA291A0BDDDF7DF69625A7013AA2D33F04DA9ABF82F7E9D8E94BE580AD12C8D 63FCF6B2413AC064E2EE4FACD8261FDE890B09105DB1913211F2ADD8DB3175BF 4F7DAAE792CA457D5BDA9C48E57DB16BB635820E8E7918C6D68C8FF6CBC2083D 60588C233F3C6CE930D90ACEC34C7DAC782B6E94089B2FBAAD34DD25A3F4091A 085C81E0B3A4CD62C93DB71E25E55AC52A539FECC3F60FB7096B918175200C67 CEB421781285E8BADA52C87B6158BF175538EFEF5C623AFB302B59173879C01C A4497761E8E7615EA8FF8FBCDE9B5E839EC883B91F87779884386A55D1CDFB73 F24B9EBC1C494216F615A0A7E85B14E7EB95B55F1DEB57E8D40B32854DF906B5 4C08706922DABF4B486706F12A7157C16E7833F09D2A55842FA414CD437330D1 CDF73B900AE4929EC594891626D7296C2C134DAE3A36593FD884A7835480989E 39911D6217C00C134E8B71860ADA02AF9CC15E391CD65F7913F93B4C71756BC6 8C2A22B82D50890043954F52905243BA961FC5AD376CC06148E70404EBB53442 1EB22E86B665718AEF948D9C5B10B7644A1BE7695D4F391126E96C50C8D2DBB8 03E041716949931C74FB881ECECBC195446C7517E2679C777D69FFA0AA32A3A1 56923A9C14D807FA4439166698 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 68 /D put dup 70 /F put dup 73 /I put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 110 /n put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 106 /bar put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 83 /S put dup 110 /n put dup 116 /t put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 30 /phi put dup 64 /partialdiff put dup 68 /D put dup 73 /I put dup 76 /L put dup 78 /N put dup 83 /S put dup 86 /V put dup 105 /i put dup 110 /n put dup 120 /x put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E 6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF 8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE 03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 AFC0E2F840512D321166547B306C592B8A01E1FA2564B9A26DAC14256414E4C8 42616728D918C74D13C349F4186EC7B9708B86467425A6FDB3A396562F7EE4D8 40B43621744CF8A23A6E532649B66C2A0002DD04F8F39618E4F572819DD34837 B5A08E643FDCA1505AF6A1FA3DDFD1FA758013CAED8ACDDBBB334D664DFF5B53 95601766758EF6E0314FC705A02FE7E5A5430F30CB95EEF1A6286542519F475E 53DE07E23471B259A72C5CD147DD077A1BCE6F9F307691080B5618064B613AB4 58938F23321D899569EC0CC8A228072C7A96ECBB72758D9C7396226B6E2A5D64 B2716AB36CF329DAE9293FE77A7EE6BF5EFF241AD58AE612164940ED839FDD61 955723F923A54A5BFB9E3B545C49A9C1CFB52DFF5DAB368ACD5C2272EB44B0BF EE4DBA13CDCF54024275A7DA1067F5A51EA4D422D11C1CB0895868F54DFC19F3 7BF722812DDD6608968E7E66F66182D62876F957240B26D64F73206EC7B454CC DDC8B9F7AF3DFAE69552F05CDD6357B2232A4A13C1F6CC21FE68218F6E006972 FCD94DAC759EDC438436568F83BEF9EBF54869EBEBB514228D85F7B46F53BC4D 023CC03583866DA4641BE5819BB7E6B8E0959BDD3585CD0BF8D3EE03417E9019 4B106ED2B42E06123CB0332D38D1BF57BE98B2B48BF140E454522B0052E30F32 7A6B7496D757DD11613CC44643AD188D5DF5D8C5DD06DA310265E085939AE926 6C892C0F6789EB91BD8428B0E10625724402CE963F7E4AF6ECAD5B0B0EC7C2A5 4C66BA9AFD5D34DDC17D57278D6884BB950F15B9CD4648BCA35D49C09BDD9EE6 03779C684DC84987F8DE53AAC391ABDECFDED21121495673F3E39D7BC75B332A B031BF90AEE3D46E86174304912BC4131AB2D0B560E3B18D1A450F88BA88152D 200A7A50E0DB14610A91B9A987BA1CFAFC70923CC6884561C93238AD61BAAED8 3C523DF35287D663BAC036B95306681EA4455A4C9DAAE38D305B69AE831D9DF3 C7AC479B10423BEFF7CE54C96D79F76F8005030963A09EEA0B98956222E851DF FF9EBB932FF3CDD11E591E221D882E2728D0AAFEE8A842594A38996E6D038587 EB41F23E62E91FFD27D71B7E7426E90AC669B2E128DD05CD7B2D0F58EC6FBE58 7062BF202E72C6E768A1250DE419A715A208272A5DFD9A080AABFD558B80E5AE 39898FAD2178A24AA4F4209A4E2BC2515C2885CB64A6353971365BDCEB6B366F 0BD52B683DA6D491383F6F92B31DD2AFEB9905C73CABADF07BCF11D78C4D0BAB C60F30A33D2FC45394D0D184955FB81FB1EAA14182E4E537F92F243F5190F691 2A5A837CFBC9307005F191CD36BD040D02AEF178EEB5208598DDF35D36E90197 61256F7068DB39C21080E104D2ABE9B5605DAA83BE05CC78BB935199FE1E19E6 39F475B566C2F69A1B99DA063900F338E40216D2C1C70F0F33E4B2039CA5A78C 7CFF214D85E5ED56EA357EEC4869CD7A08CD9BB8A304B8A6188C4D8589A196DF 5E2E0660BAD9930F8B8210B2F2613ED93C42FF5209787A810001DBFF497E55E2 91552583D84D2DE47C109AB5F55585FFECA50F951CCF11AEEF54B0C6770F59AE 70260E4FA88DD36CD80ABC2AD05DB2B99DF1448785A6D731B8F2AAA440247115 ECB907BD1B540318222277F23F6DC45BF8D490C331971A26CD8519DCD0CD9268 CADEEAB018BEFBEC054101C658D42BD39B3CC639ECFBB06D84E45676A5B6BF7A 22404B426681EE7AAC2FCE4F572091814C1772A445C4ED7919FC9D8CF0703E95 51ED33CA5A282C27AAC4233682AD2476BC457D4DD31CC48829F12E6D964DAB45 CB82DB190408DC816B075F614C7931D689B95B6906E0F518873A766BECE84CF7 D816AA67CDC4B5B3945718BC88CADF62B5F612B89E7C06DE6A394DED9D944595 49876741A45D4B1AE2C958C2750BCBC84C9EC9CBC34AA416080FD2C86A76CA25 C39FD2DF1BA238CF33EE03FD4EE68615F460BDA5837AF046AC1C95AA609DD191 BB1EDA8EFA1E1C0063838952808A1EA5E5A06A20B8C89CB780B018E2C5F58DC7 46D59FDCFDC2D773DED6D1E2B7F09EB707BEABA9B079028317A175796AC9C99F B96C1F6863F67A227C62AE9F589403F8899BA0A16C7EACFD17676595C1B4DF93 AAC0F9B7E58177EA7013C5ADD1DB24E6A1372320E19AD7D93F04D4E98D03274A 305BCF5B391DCD5D08411B25C0054F0741B2FDFA113D99F28039E672CBE59817 840183D6D99908C1AC7A321E9639712145C65B9FA49750746D00D3BD4FCF06CD 2B0BCB67630CA9590AAE0388C034AC47CF89B54542190D4356D83246B28C3CA2 E7BF845E2E8064DE810FEFF0A0CBC8A40EC1D355050547309693B2CB3AC4ABAD 39B54EA48CC8C4C394AA9C7E77F5AD4E40F310BD5BAAAC753EAA72EC3DBCB6D5 E855A69D357A9809F775AADA98A2903FA03EA96227F9DFCE70715B5EF652A61C E6AFDBA6622507B8DBD47A51F99DC7ACDA97F06CBF797222963D6F7858016199 03BE68FA9D342A1749A3760E41A7306EF48AFFE491F4229867A28E6C132186FB 7E0D7CBEF87DB7D20A0346EBD1119777BD6498B837479B6F627438C8DDC066CA E37227451CC6A557829F67E411E3EE2876AE8BE9BC6DBBB72F39351E0EA05043 727290E3C9FEB89EBE3118E726EE36A0C543F5544C44A28184BC4C6E5A947F9A A88D3E2A63C5CE5C61FC3E70AD1EAA71F9D99CD15181F25968F63AE9E6887B0C 1654F0C4EC8010A7D3A89F69D6176DEC0BFB7EA324922A3F9C341D4A0EECC3F6 FC6166D69E4273B71C5EDF965D3A39AB2FC5A325435059CF4635512B9FA77883 2E1EAEE7BDA8B4A5B8810B18A2DC8B55E50F28E44AACE8A60D51C69E8D161225 680C96EB8D99AF085DBFFFDFE000B1546CA9A08803EFDAA66F5285AD0A67C9DC B618577B02205E1F5ECE946DEE171BEC741C6B2F994B94F820D2877C6176D441 679E9678E3983342B04F76E1A888E136237B6C13294C3918F7E6DBB4629E34A1 077197DFC1205F0749B57F4F423B1D96F90EAC52F444FBCC5D8A58D3306D7CFE 24860433327021C18AC873D21FE140A9373EEDA30F3FBDC594BB0AD469A046A3 44BD17CE20B8C249FAA54D7668DECF4E5565D91564BC177F8A736044283B36DD 0EC1719498BD7171C2F3ECA32A46AEAED541AA1C7D3A77FA71279A0C91579E78 11881957E4CE8B5D86D47040252388E3EA80A273BE587A625761BDAED7D24F99 7127ABBC4CBCDFB0499B806BF30BB282EBA4F583868BD38054825DB05A65D0B7 5CE5435C7B160EBBB843CEBCE91D1B88C00A25429C9E900FA9E556F6A7371DE1 4C806C01BDD6BB8579340A79B010ED318FB4D6AC71368883D11242C4FDA8D056 AED9CD62480E71E417ABBAAB4D8084092CD5AB9FCA8AFB48A2B144280297075C B3CFB52E30D95D7CAE13EB0454239C1D40505ED6391763A349BB479CB5E32D7D 71E76DB33CAFF66DA50C8A317223F391F513A08EAA73D9D40819F7ECE2729801 D2967CEA51DA76E8638654FC156584CF2E7FD113B5BB975E89E02163ABD57529 6D4023B4BA 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 11 /ff put dup 19 /acute put dup 28 /oslash put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 90 /Z put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put dup 122 /z put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (HS_271003.dvi) @start /Fa 134[44 1[44 44 44 44 44 44 3[44 44 44 44 1[44 44 44 44 44 44 1[44 44 32[44 17[44 46[{}21 83.022 /CMTT10 rf /Fb 128[42 3[42 34 40 39 55 1[45 28 34 35 38 42 42 47 68 21 1[25 25 42 38 25 38 42 38 38 42 12[59 47 61 64 1[64 1[74 52 2[32 62 64 54 56 63 59 1[62 6[25 6[42 4[25 30 25 31[47 51 11[{}48 83.022 /CMTI10 rf /Fc 207[18 47[48{}2 49.8132 /CMSY6 rf /Fd 173[61 14[59 67[{}2 66.4176 /CMBX8 rf /Fe 252[77 3[{}1 99.6264 /MSAM10 rf /Ff 138[37 1[29 29 3[38 1[20 33 25 22 36 76[36 3[31 37 6[26 15[{}13 49.8132 /CMMI6 rf /Fg 128[50 4[40 47 45 65 45 52 32 40 41 45 50 50 55 80 25 45 30 30 50 45 30 45 50 45 45 50 3[30 1[30 3[97 1[72 70 55 71 1[66 1[72 1[61 2[38 72 1[64 66 1[70 69 72 5[30 1[50 50 1[50 50 50 50 50 50 2[30 35 30 2[40 40 25[86 1[55 60 11[{}61 99.6264 /CMTI12 rf /Fh 205[30 30 30 12[50 35[{}4 49.8132 /CMR6 rf /Fi 142[100 100 66 66 4[47 47 13[55 1[144 5[47 1[105 10[61 61 2[87 87 14[87 87 18[75 75 75 75 6[73 73 59 59 2[55 33 47 47 58 58 4[42 42 46 46{}34 99.6264 /CMEX10 rf /Fj 129[35 16[59 3[20 4[39 6[20 1[20 29[55 7[35 35 35 35 35 35 4[55 1[27 27 4[59 12[35 22[{}18 66.4176 /CMR8 rf /Fk 141[83 1[83 1[50 2[50 28 39 39 50 50 9[66 66 5[62 6[82 1[69 76 2[84 1[72 1[77 52 65 6[50 4[0 2[66 66 100 15[100 7[77 3[77 77 1[77 3[50 5[77 5[77 28 77{}35 99.6264 /CMSY10 rf /Fl 170[58 55 43 57 60 1[60 58 70 1[60 1[28 58 1[50 52 59 55 54 58 7[38 38 38 38 38 38 38 38 38 38 48[{}27 74.7198 /CMR9 rf /Fm 133[33 1[40 51 34 41 25 33 32 1[36 1[43 62 21 37 29 24 41 1[34 33 36 31 1[37 10[41 9[48 2[31 58 2[52 1[50 53 1[37 2[35 1[20 25[44 5[40 2[31 35 42 41 41 2[35 1[29 31 1[40 45 11[{}43 66.4176 /CMMI8 rf /Fn 149[20 38[37 3[55 12[47 71 19 12[35 1[71 11[55 55 16[35 2[55{}12 66.4176 /CMSY8 rf /Fo 133[45 48 55 70 47 56 35 46 44 43 49 47 58 85 29 51 40 33 56 47 48 45 51 42 41 51 10[57 66 57 60 74 77 63 75 78 94 66 2[43 81 77 63 72 81 70 74 73 51 1[76 49 76 27 27 24[61 63 61 58 1[42 55 1[55 43 48 59 57 56 2[48 43 39 43 51 55 62 11[{}71 99.6264 /CMMI12 rf /Fp 128[49 49 2[49 43 51 51 70 51 54 38 38 38 51 54 49 54 81 27 51 30 27 54 49 30 43 54 43 54 49 27 1[49 27 49 27 3[100 73 73 70 54 72 76 66 76 73 89 61 76 1[35 73 77 64 66 75 70 69 73 1[46 1[76 1[27 27 49 49 49 49 49 49 49 49 49 49 49 27 33 27 76 1[38 38 27 3[81 49 27 4[49 5[49 49 1[49 4[81 54 54 57 1[76 70 7[61{}92 99.6264 /CMR12 rf /Fq 132[55 50 61 3[61 59 46 60 1[56 63 61 74 51 2[30 61 1[53 56 62 59 1[61 12[78 1[80 1[74 2[99 3[40 5[78 16[55 55 2[32 46[{}28 99.6264 /CMCSC10 rf /Fr 206[28 49[{}1 41.511 /CMR5 rf /Fs 255[45{}1 41.511 /CMSY5 rf /Ft 145[37 110[{}1 41.511 /CMMI5 rf /Fu 205[33 33 49[{}2 58.1154 /CMR7 rf /Fv 149[20 105[52{}2 58.1154 /CMSY7 rf /Fw 149[23 84[65 20[65{}3 83.022 /CMSY10 rf /Fx 139[25 5[41 26[41 83[{}3 58.1154 /CMMI7 rf /Fy 173[72 82[{}1 83.022 /CMBX10 rf /Fz 135[47 9[50 4[29 18[48 2[51 4[67 1[57 2[36 4[69 3[44 33[49 30[{}11 83.022 /CMMI10 rf /FA 134[51 2[51 51 49 38 50 1[46 53 51 62 43 53 1[25 51 53 44 46 52 49 48 51 10[68 68 1[51 4[68 82 3[34 2[59 1[69 65 1[68 7[46 46 4[46 46 1[46 1[27 31 27 44[{}39 83.022 /CMCSC10 rf /FB 128[42 3[42 37 44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 1[23 46 42 25 37 46 37 46 42 3[23 1[23 1[62 1[85 62 62 60 46 61 1[57 1[62 76 52 65 43 30 62 65 54 57 63 60 59 62 3[65 2[23 42 42 42 42 42 42 42 42 42 42 1[23 28 23 65 1[32 32 11[42 8[42 7[48 9[69 1[{}73 83.022 /CMR10 rf /FC 133[50 59 3[62 44 44 46 1[62 56 62 93 31 2[31 62 56 34 51 1[50 1[54 6[68 4[86 78 62 84 84 77 84 88 106 67 2[42 88 88 70 74 86 81 80 85 6[31 1[56 56 56 56 56 56 56 56 2[31 33[62 12[{}49 99.6264 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 408 724 a FC(ABSENCE)47 b(OF)i(QUANTUM)g(ST)-9 b(A)g(TES)47 b(CORRESPONDING)774 841 y(TO)i(UNST)-9 b(ABLE)47 b(CLASSICAL)i(CHANNELS:)488 957 y(HOMOGENEOUS)f(POTENTIALS)f(OF)i (DEGREE)e(ZER)m(O)1163 1206 y FB(IRA)28 b(HERBST)g(AND)g(ERIK)f (SKIBSTED)685 1447 y FA(Abstra)n(ct.)41 b FB(W)-7 b(e)34 b(dev)n(elop)e(a)i(general)e(theory)g(of)i(absence)f(of)g(quan)n(tum) 685 1547 y(states)k(corresp)r(onding)f(to)i(unstable)g(classical)e(c)n (hannels.)67 b(A)38 b(principal)685 1646 y(example)30 b(treated)h(in)g(detail)g(is)f(the)i(follo)n(wing:)42 b(Consider)30 b(a)g(real-v)-5 b(alued)685 1746 y(p)r(oten)n(tial)31 b Fz(V)51 b FB(on)31 b Fy(R)1329 1716 y Fx(n)1374 1746 y FB(,)h Fz(n)d Fw(\025)h FB(2,)i(whic)n(h)f(is)g(smo)r(oth)h(outside)f (zero)f(and)i(ho-)685 1846 y(mogeneous)22 b(of)h(degree)g(zero.)34 b(Supp)r(ose)24 b(that)g(the)g(restriction)e(of)i Fz(V)42 b FB(to)24 b(the)685 1945 y(unit)k(sphere)f Fz(S)1175 1915 y Fx(n)p Fv(\000)p Fu(1)1333 1945 y FB(is)g(a)g(Morse)g(function.) 37 b(W)-7 b(e)28 b(pro)n(v)n(e)e(that)i(there)g(are)e(no)685 2045 y Fz(L)742 2015 y Fu(2)779 2045 y FB({solutions)32 b(to)i(the)h(Sc)n(hr\177)-42 b(odinger)32 b(equation)h Fz(i@)2310 2057 y Fx(t)2339 2045 y Fz(\036)h FB(=)g(\()p Fw(\000)p FB(2)2660 2015 y Fv(\000)p Fu(1)2748 2045 y FB(\001)23 b(+)f Fz(V)d FB(\))p Fz(\036)685 2144 y FB(whic)n(h)29 b(asymptotically)e(in)i(time)h(are)e(concen)n(trated)f(near)h(lo)r(cal) h(maxima)685 2244 y(or)38 b(saddle)h(p)r(oin)n(ts)g(of)h Fz(V)1480 2260 y Fv(j)p Fx(S)1544 2243 y Ft(n)p Fs(\000)p Fr(1)1662 2244 y FB(.)72 b(Consequen)n(tly)38 b(all)h(states)g(concen)n (trate)685 2344 y(asymptotically)24 b(in)h(time)h(near)e(the)i(lo)r (cal)e(minima.)36 b(Short-range)23 b(p)r(ertur-)685 2443 y(bations)k(are)f(included.)1639 2859 y Fq(Contents)486 3034 y Fp(1.)97 b(In)m(tro)s(duction)2134 b(2)486 3150 y(1.1.)97 b(A)32 b(generalization)1896 b(6)486 3266 y(2.)97 b(T)-8 b(ec)m(hnical)35 b(conditions)e(and)g(outline)g(of)f(pro)s(of) 918 b(9)486 3382 y(2.1.)97 b(Outline)33 b(of)f(pro)s(of)g(of)g(Theorem) i(1.1)1176 b(12)486 3499 y(2.2.)97 b(Classical)34 b(\000)2079 b(12)486 3615 y(2.3.)97 b(Quan)m(tum)33 b(\000)2045 b(14)486 3731 y(2.4.)97 b(Implemen)m(ting)35 b(the)e(uncertain)m(t)m(y)h (principle)872 b(15)486 3847 y(3.)97 b(Preliminaries)2060 b(15)486 3963 y(4.)97 b Fo(t)694 3927 y Fn(\000)p Fm(\016)787 3963 y Fp({lo)s(calization)1956 b(19)486 4080 y(5.)97 b(\000)32 b(and)h(its)g(lo)s(calization)1714 b(23)486 4196 y(6.)97 b(Mourre)33 b(theory)g(for)f(\000)1758 b(29)486 4312 y(7.)97 b(Pro)s(of)32 b(of)g(Theorem)i(1.1)1703 b(31)486 4428 y(8.)97 b(Pro)s(of)32 b(of)g(Theorem)i(1.2)1703 b(32)486 4545 y(References)2344 b(38)p 386 5432 499 4 v 486 5523 a FB(E.)23 b(Skibsted)h(is)g(\(partially\))g(supp)r(orted)g (b)n(y)g(MaPh)n(ySto)e({)i(A)g(Net)n(w)n(ork)f(in)h(Mathematical)386 5623 y(Ph)n(ysics)i(and)i(Sto)r(c)n(hastics,)f(funded)h(b)n(y)f(The)h (Danish)g(National)f(Researc)n(h)f(F)-7 b(oundation.)1861 5722 y Fl(1)p eop end %%Page: 2 2 TeXDict begin 2 1 bop 386 259 a Fl(2)793 b(IRA)24 b(HERBST)i(AND)e (ERIK)h(SKIBSTED)1479 459 y Fp(1.)49 b Fq(Intr)n(oduction)486 633 y Fp(The)33 b(purp)s(ose)g(of)f(this)h(pap)s(er)f(is)h(to)f(sho)m (w)i(in)e(a)g(class)i(of)e(mo)s(dels)h(that)f(there)386 749 y(are)45 b(no)g(quan)m(tum)i(states)f(corresp)s(onding)g(to)f (unstable)i(classical)g(c)m(hannels.)386 866 y(W)-8 b(e)37 b(consider)i(the)e(follo)m(wing)h(general)f(situation:)53 b(Supp)s(ose)38 b Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))37 b(is)h(a)f(real)386 982 y(classical)d(Hamiltonian)f(in)g Fo(C)1513 946 y Fn(1)1587 982 y Fp(\(\()p FC(R)1747 946 y Fm(n)1816 982 y Fk(n)22 b(f)p Fp(0)p Fk(g)p Fp(\))f Fk(\002)i FC(R)2280 946 y Fm(n)2326 982 y Fp(\),)33 b Fo(n)28 b Fk(\025)g Fp(2,)33 b(satisfying)1524 1170 y Fo(x)22 b Fk(\001)g(r)1734 1185 y Fm(x)1778 1170 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h(0)386 1358 y(in)g(a)f(neigh)m(b)s(orho)s(o)s(d)g(of)g(a)g(p)s(oin)m(t)h(\()p Fo(!)1709 1373 y Fj(0)1748 1358 y Fo(;)17 b(\030)1835 1373 y Fj(0)1874 1358 y Fp(\))27 b Fk(2)h Fo(S)2099 1322 y Fm(n)p Fn(\000)p Fj(1)2248 1358 y Fk(\002)12 b FC(R)2421 1322 y Fm(n)2468 1358 y Fp(.)41 b(Supp)s(ose)29 b(in)e(addition)386 1474 y(that)41 b(this)i(neigh)m(b)s(orho)s(o)s(d)e(is)i(conic)f(in)g (the)g Fo(x)p Fp({v)-5 b(ariable)42 b(and)g(that)g(the)g(orbit)386 1590 y(\(0)p Fo(;)17 b Fk(1)p Fp(\))45 b Fk(3)i Fo(t)f Fk(!)g Fp(\()p Fo(x)p Fp(\()p Fo(t)p Fp(\))p Fo(;)17 b(\030)5 b Fp(\()p Fo(t)p Fp(\)\))46 b(=)g(\()p Fo(tk)1777 1605 y Fj(0)1816 1590 y Fo(!)1877 1605 y Fj(0)1916 1590 y Fo(;)17 b(\030)2003 1605 y Fj(0)2042 1590 y Fp(\))43 b(with)h Fo(k)2407 1605 y Fj(0)2493 1590 y Fo(>)i Fp(0)d(is)h(a)f (solution)h(to)386 1707 y(Hamilton's)33 b(equations)1112 1875 y Fo(dx)p 1112 1920 107 4 v 1122 2011 a(dt)1255 1943 y Fp(=)28 b Fk(r)1442 1958 y Fm(\030)1480 1943 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(;)1910 1875 y(d\030)p 1910 1920 99 4 v 1916 2011 a(dt)2045 1943 y Fp(=)28 b Fk(\000r)2309 1958 y Fm(x)2353 1943 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)386 2160 y Fp(or)32 b(equiv)-5 b(alen)m(tly)d(,)1064 2349 y Fk(r)1147 2364 y Fm(x)1190 2349 y Fo(h)p Fp(\()q Fo(!)1346 2364 y Fj(0)1385 2349 y Fo(;)17 b(\030)1472 2364 y Fj(0)1510 2349 y Fp(\))28 b(=)g(0)p Fo(;)114 b Fk(r)1953 2364 y Fm(\030)1990 2349 y Fo(h)p Fp(\()q Fo(!)2146 2364 y Fj(0)2185 2349 y Fo(;)17 b(\030)2272 2364 y Fj(0)2310 2349 y Fp(\))28 b(=)g Fo(k)2531 2364 y Fj(0)2570 2349 y Fo(!)2631 2364 y Fj(0)2670 2349 y Fo(:)477 b Fp(\(1.1\))386 2537 y(W)-8 b(e)32 b(consider)i(situations) f(in)f(whic)m(h)h(for)f(eac)m(h)h(energy)g Fo(E)38 b Fp(near)32 b Fo(E)2846 2552 y Fj(0)2913 2537 y Fp(=)c Fo(h)p Fp(\()p Fo(!)3172 2552 y Fj(0)3211 2537 y Fo(;)17 b(\030)3298 2552 y Fj(0)3337 2537 y Fp(\))386 2653 y(there)28 b(is)g(a)f(\(t)m(ypically)j(unique\))f(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))27 b Fk(2)i Fo(S)2308 2617 y Fm(n)p Fn(\000)p Fj(1)2456 2653 y Fk(\002)12 b FC(R)2629 2617 y Fm(n)2704 2653 y Fp(near)27 b(\()p Fo(!)3014 2668 y Fj(0)3053 2653 y Fo(;)17 b(\030)3140 2668 y Fj(0)3179 2653 y Fp(\))28 b(de-)386 2769 y(p)s(ending)i(smo)s(othly)g(on)g Fo(E)35 b Fp(suc)m(h)c(that)f (the)g(ab)s(o)m(v)m(e)g(structure)h(p)s(ersists,)h(namely)1230 2957 y Fo(h)p Fp(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))28 b(=)g Fo(E)6 b(;)1112 b Fp(\(1.2\))1230 3108 y Fk(r)1313 3123 y Fm(x)1357 3108 y Fo(h)p Fp(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))28 b(=)f(0)p Fo(;)1015 b Fp(\(1.3\))1230 3259 y Fk(r)1313 3274 y Fm(\030)1351 3259 y Fo(h)p Fp(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))28 b(=)f Fo(k)s Fp(\()p Fo(E)6 b Fp(\))p Fo(!)t Fp(\()p Fo(E)g Fp(\))p Fo(:)643 b Fp(\(1.4\))386 3448 y(Although)36 b(w)m(e)g(shall)h(not)e (elab)s(orate)h(here,)h(w)m(e)f(remark)h(that)e(one)h(ma)m(y)g(easily) 386 3564 y(deriv)m(e)e(a)e(criterion)i(for)e(\(1.2\){\(1.4\))f(using)i (the)g(implicit)h(function)f(theorem.)486 3680 y(Let)h(us)h(restrict)h (atten)m(tion)f(to)f(the)h(constan)m(t)g(energy)h(surface)f Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))31 b(=)g Fo(E)386 3796 y Fp(and)37 b(to)g(v)-5 b(alues)38 b(of)f(\()6 b(^)-55 b Fo(x;)17 b(\030)5 b(;)17 b(E)6 b Fp(\))36 b(close)i(to)f(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\))p Fo(;)17 b(E)2475 3811 y Fj(0)2515 3796 y Fp(\))o(.)58 b(\(Here)37 b(and)h(hence-)386 3913 y(forth)g(^)-55 b Fo(x)28 b Fp(=)g Fk(j)p Fo(x)p Fk(j)925 3877 y Fn(\000)p Fj(1)1019 3913 y Fo(x)p Fp(.\))44 b(In)m(tro)s(duce)33 b(a)g(c)m(hange)g(of)f(v)-5 b(ariables)942 4092 y Fo(x)28 b Fp(=)g Fo(x)1184 4107 y Fm(n)1231 4092 y Fp(\()p Fo(!)t Fp(\()p Fo(E)6 b Fp(\))22 b(+)g Fo(u)p Fp(\))o Fo(;)114 b(\030)32 b Fp(=)c Fo(\030)5 b Fp(\()o Fo(E)h Fp(\))22 b(+)g Fo(\021)k Fp(+)c Fo(\026!)t Fp(\()o Fo(E)6 b Fp(\);)942 4244 y Fo(u)22 b Fk(\001)g Fo(!)t Fp(\()o Fo(E)6 b Fp(\))28 b(=)f Fo(\021)f Fk(\001)c Fo(!)t Fp(\()o Fo(E)6 b Fp(\))28 b(=)f(0)p Fo(:)3174 4175 y Fp(\(1.5\))386 4442 y(This)43 b(amoun)m(ts)h(to)e(considering)i(co)s(ordinates)e(\()p Fo(u;)17 b(x)2391 4457 y Fm(n)2438 4442 y Fo(;)g(\021)t(;)g(\026)p Fp(\))43 b Fk(2)i FC(R)2913 4406 y Fm(n)p Fn(\000)p Fj(1)3078 4442 y Fk(\002)30 b FC(R)e Fk(\002)386 4558 y FC(R)470 4522 y Fm(n)p Fn(\000)p Fj(1)607 4558 y Fk(\002)p FC(R)p Fp(.)40 b(W)-8 b(e)22 b(can)g(solv)m(e)h(the)f(equation)h Fo(h)p Fp(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))22 b(+)g Fo(u;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\))22 b(+)g Fo(\021)k Fp(+)c Fo(\026!)t Fp(\()o Fo(E)6 b Fp(\)\))27 b(=)386 4674 y Fo(E)38 b Fp(for)33 b Fo(\026)f Fp(using)h(the)g(implicit)h (function)f(theorem,)g(b)s(ecause)997 4862 y Fo(@)1048 4877 y Fm(\026)1095 4862 y Fo(h)p Fp(\()p Fo(!)t Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\))22 b(+)g Fo(\026!)t Fp(\()o Fo(E)6 b Fp(\)\))2088 4891 y Fn(j)p Fm(\026)p Fj(=0)2272 4862 y Fp(=)27 b Fo(k)s Fp(\()p Fo(E)6 b Fp(\))28 b Fo(>)g Fp(0)386 5063 y(for)43 b Fo(E)49 b Fp(near)44 b Fo(E)967 5078 y Fj(0)1007 5063 y Fp(.)76 b(W)-8 b(e)44 b(obtain)f Fo(\026)j Fp(=)g Fk(\000)p Fo(g)t Fp(\()p Fo(u;)17 b(\021)t(;)g(E)6 b Fp(\))42 b(where)j Fo(g)i Fp(is)d(smo)s(oth)f(in)h(a)386 5179 y(neigh)m(b)s(orho)s(o)s(d) 39 b(of)g(\(0)p Fo(;)17 b Fp(0)p Fo(;)g(E)1419 5194 y Fj(0)1458 5179 y Fp(\))39 b(and)h Fo(g)t Fp(\()o(0)p Fo(;)17 b Fp(0)p Fo(;)g(E)2078 5194 y Fj(0)2117 5179 y Fp(\))40 b(=)f(0.)64 b(After)40 b(in)m(tro)s(ducing)g(the)386 5295 y(\\new)27 b(time")g Fo(\034)39 b Fp(=)27 b(ln)17 b Fo(x)1231 5310 y Fm(n)1279 5295 y Fp(\()p Fo(t)p Fp(\))27 b(=)h(ln)17 b(\()p Fo(x)p Fp(\()p Fo(t)p Fp(\))22 b Fk(\001)g Fo(!)t Fp(\()p Fo(E)6 b Fp(\)\))26 b(Hamilton's)h(equations)g(reduce) 386 5411 y(to)888 5588 y Fo(u)22 b Fp(+)1074 5520 y Fo(du)p 1074 5565 107 4 v 1075 5656 a(d\034)1217 5588 y Fp(=)28 b Fk(r)1404 5603 y Fm(\021)1446 5588 y Fo(g)t Fp(\()o Fo(u;)17 b(\021)t(;)g(E)6 b Fp(\))o Fo(;)1997 5520 y(d\021)p 1996 5565 105 4 v 1996 5656 a(d\034)2138 5588 y Fp(=)27 b Fk(\000r)2401 5603 y Fm(u)2447 5588 y Fo(g)t Fp(\()o Fo(u;)17 b(\021)t(;)g(E)6 b Fp(\))o Fo(:)301 b Fp(\(1.6\))p eop end %%Page: 3 3 TeXDict begin 3 2 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)809 b(3)386 459 y Fp(\(See)39 b([A2,)h(p.)62 b(243].\))f(After)39 b(linearization)g(of)f(these)i(equations)g(around) e(the)386 575 y(\014xed)c(p)s(oin)m(t)e(\()p Fo(u;)17 b(\021)t Fp(\))27 b(=)g(\(0)p Fo(;)17 b Fp(0\))32 b(w)m(e)i(obtain)e (with)h Fo(w)d Fp(=)e(\()p Fo(u;)17 b(\021)t Fp(\))690 727 y Fo(dw)p 690 772 124 4 v 699 863 a(d\034)851 795 y Fp(=)28 b Fo(B)5 b Fp(\()p Fo(E)h Fp(\))p Fo(w)s Fp(;)113 b Fo(B)5 b Fp(\()p Fo(E)h Fp(\))28 b(=)1766 654 y Fi(\022)1879 735 y Fp(0)122 b Fo(I)1839 851 y Fk(\000)p Fo(I)92 b Fp(0)2101 654 y Fi(\023)2175 795 y Fo(A)p Fp(\()p Fo(E)6 b Fp(\))22 b Fk(\000)2523 654 y Fi(\022)2597 735 y Fo(I)91 b Fp(0)2598 851 y(0)84 b(0)2779 654 y Fi(\023)2853 795 y Fo(;)680 1071 y(A)p Fp(\()p Fo(E)6 b Fp(\))28 b(=)1039 931 y Fi(\022)1112 1011 y Fo(g)1159 1026 y Fm(u;u)1347 1011 y Fo(g)1394 1026 y Fm(u;\021)1114 1128 y Fo(g)1161 1143 y Fm(\021)r(;u)1349 1128 y Fo(g)1396 1143 y Fm(\021)r(;\021)1496 931 y Fi(\023)1570 1071 y Fo(:)3174 933 y Fp(\(1.7\))386 1291 y(Here)45 b(the)g(real)f(symmetric)j(matrix)d Fo(A)p Fp(\()q Fo(E)6 b Fp(\))44 b(of)g(second)h(order)g(deriv)-5 b(ativ)m(es)46 b(is)386 1407 y(ev)-5 b(aluated)27 b(at)g(\(0)p Fo(;)17 b Fp(0)p Fo(;)g(E)6 b Fp(\))o(.)41 b(W)-8 b(e)28 b(assume)g(all)f(eigen)m(v)-5 b(alues)29 b(of)d Fo(B)5 b Fp(\()p Fo(E)h Fp(\))27 b(ha)m(v)m(e)h(nonzero)386 1523 y(real)33 b(part)f(\(the)h(h)m(yp)s(erb)s(olic)h(case\).)44 b(These)35 b(eigen)m(v)-5 b(alues)34 b(are)f(easily)h(pro)m(v)m(ed)g (to)386 1640 y(come)39 b(in)g(quadruples,)j Fo(\025;)17 b Fk(\000)p Fp(1)26 b Fk(\000)g Fo(\025)p Fp(,)40 b(and)f(their)g (complex)h(conjugates)f(\(if)f Fo(\025)g Fp(is)386 1756 y(not)e(real\).)53 b(If)35 b(all)h(eigen)m(v)-5 b(alues)38 b(of)d Fo(B)5 b Fp(\()p Fo(E)h Fp(\))36 b(ha)m(v)m(e)h(negativ)m(e)g (real)f(part)g(then)g(this)386 1872 y(corresp)s(onds)h(to)e(a)h(stable) h(c)m(hannel.)54 b(W)-8 b(e)36 b(prefer)h(the)f(w)m(ord)g(c)m(hannel)h (b)s(ecause)386 1988 y(in)h(the)g(case)h(considered)g Fo(x)1427 2003 y Fm(n)1475 1988 y Fp(\()p Fo(t)p Fp(\))e(gro)m(ws)i (linearly)f(in)g(time.)60 b(If)38 b(at)f(least)h(one)g(of)386 2105 y(the)43 b(eigen)m(v)-5 b(alues)44 b(of)e Fo(B)5 b Fp(\()p Fo(E)h Fp(\))43 b(has)g(a)f(p)s(ositiv)m(e)i(real)e(part)h (then)g(the)g(usual)g(sta-)386 2221 y(ble/unstable)i(manifold)e (theorem)g(sho)m(ws)i(that)e(there)h(are)f(alw)m(a)m(ys)h(classical)386 2337 y(orbits)c(\(on)h(the)f(stable)h(manifold\))g(for)e(whic)m(h)j(\() 6 b(^)-55 b Fo(x)p Fp(\()p Fo(t)p Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(t)p Fp(\))q(\))40 b Fk(!)h Fp(\()o Fo(!)t Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))386 2453 y(for)40 b Fo(t)h Fk(!)f(1)g Fp(\(throughout)g(this)h (pap)s(er)f(w)m(e)h(use)h(the)e(con)m(v)m(en)m(tion)j Fo(t)e Fk(!)f(1)g Fp(to)386 2570 y(mean)47 b Fo(t)53 b Fk(!)e Fp(+)p Fk(1)c Fp(\).)86 b(In)47 b(this)h(situation)f(the)g (question)i(is,)i(do)c(there)g(exist)386 2686 y(quan)m(tum)34 b(states)g(whose)g(propagation)e(is)i(go)m(v)m(erned)g(b)m(y)g(a)e (self-adjoin)m(t)i(quan-)386 2802 y(tization)28 b Fo(H)36 b Fp(of)27 b Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(on)g Fo(L)1466 2766 y Fj(2)1522 2802 y Fp(\()p FC(R)1644 2766 y Fm(n)1691 2802 y Fp(\))g(\(p)s(ossibly)h(with)g(the)f (singularit)m(y)i(at)d Fo(x)h Fp(=)g(0)386 2918 y(remo)m(v)m(ed\))k (whic)m(h)f(exhibit)h(this)e(b)s(eha)m(vior?)44 b(W)-8 b(e)30 b(will)h(answ)m(er)g(this)g(question)g(in)386 3034 y(the)i(negativ)m(e.)486 3151 y(T)-8 b(o)23 b(b)s(e)g(precise,)k (let)d(us)g(\014rst)g(\014x)g(a)f(\(small\))g(neigh)m(b)s(orho)s(o)s(d) g Fk(U)2710 3166 y Fj(0)2778 3151 y Fk(\022)28 b Fp(\()p FC(R)3005 3115 y Fm(n)3055 3151 y Fk(n)s(f)p Fp(0)p Fk(g)o Fp(\))s Fk(\002)386 3267 y FC(R)470 3231 y Fm(n)554 3267 y Fp(of)36 b(\()p Fo(k)s Fp(\()p Fo(E)871 3282 y Fj(0)911 3267 y Fp(\))p Fo(!)1010 3282 y Fj(0)1049 3267 y Fo(;)17 b(\030)1136 3282 y Fj(0)1175 3267 y Fp(\).)57 b(Then)38 b(w)m(e)h(consider)f(a)f(small)h(op)s(en)f(neigh)m(b)s(orho)s(o)s(d)g Fo(I)3335 3282 y Fj(0)386 3383 y Fp(of)32 b Fo(E)569 3398 y Fj(0)641 3383 y Fp(and)h(states)g(of)f(the)h(form)g Fo( )e Fp(=)d Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )37 b Fp(with)c Fo(f)38 b Fk(2)28 b Fo(C)2618 3347 y Fn(1)2611 3408 y Fj(0)2693 3383 y Fp(\()p Fo(I)2774 3398 y Fj(0)2813 3383 y Fp(\))33 b(suc)m(h)h(that:)544 3533 y(F)-8 b(or)32 b(all)g Fo(g)901 3548 y Fj(1)940 3533 y Fo(;)17 b(g)1031 3548 y Fj(2)1098 3533 y Fk(2)28 b Fo(C)1269 3492 y Fn(1)1262 3558 y Fj(0)1344 3533 y Fp(\()p FC(R)1466 3492 y Fm(n)1512 3533 y Fp(\))544 3694 y Fk(k)594 3614 y Fi(\010)652 3694 y Fo(g)699 3709 y Fj(1)738 3614 y Fi(\000)784 3694 y Fo(t)819 3653 y Fn(\000)p Fj(1)913 3694 y Fo(x)968 3614 y Fi(\001)1037 3694 y Fk(\000)22 b Fo(g)1183 3709 y Fj(1)1222 3694 y Fp(\()p Fo(k)s Fp(\()p Fo(H)8 b Fp(\))p Fo(!)t Fp(\()o Fo(H)g Fp(\))o(\)1)1794 3709 y Fm(I)1825 3718 y Fh(0)1863 3694 y Fp(\()p Fo(H)g Fp(\))2028 3614 y Fi(\011)2086 3694 y Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(k)28 b(!)f Fp(0)32 b(for)g Fo(t)c Fk(!)f(1)p Fo(;)544 3845 y Fk(kf)p Fo(g)691 3860 y Fj(2)730 3845 y Fp(\()p Fo(p)p Fp(\))22 b Fk(\000)g Fo(g)1023 3860 y Fj(2)1063 3845 y Fp(\()o Fo(\030)5 b Fp(\()p Fo(H)j Fp(\))o(\)1)1399 3860 y Fm(I)1430 3869 y Fh(0)1468 3845 y Fp(\()p Fo(H)g Fp(\))p Fk(g)p Fo( )t Fp(\()o Fo(t)p Fp(\))q Fk(k)27 b(!)g Fp(0)33 b(for)f Fo(t)c Fk(!)f(1)p Fp(;)544 4008 y Fo( )t Fp(\()p Fo(t)p Fp(\))h(=)f Fo(e)898 3967 y Fn(\000)p Fm(itH)1070 4008 y Fo( )t(;)114 b(p)28 b Fp(=)g Fk(\000)p Fo(i)p Fk(r)1652 4023 y Fm(x)1696 4008 y Fo(;)3174 3777 y Fp(\(1.8\))386 4167 y(while)473 4220 y Fi(Z)573 4246 y Fn(1)529 4445 y Fj(1)664 4355 y Fo(t)699 4314 y Fn(\000)p Fj(1)810 4271 y Fi(\015)810 4330 y(\015)866 4355 y Fo(a)917 4314 y Fm(w)973 4275 y Fi(\000)1019 4355 y Fo(t)1054 4314 y Fn(\000)p Fj(1)1149 4355 y Fo(x;)17 b(p)1297 4275 y Fi(\001)1342 4355 y Fo( )t Fp(\()p Fo(t)p Fp(\))1520 4271 y Fi(\015)1520 4330 y(\015)1576 4297 y Fj(2)1632 4355 y Fo(dt)27 b(<)h Fk(1)k Fp(for)g(all)h Fo(a)28 b Fk(2)g Fo(C)2516 4314 y Fn(1)2509 4380 y Fj(0)2590 4355 y Fp(\()p Fk(U)2690 4370 y Fj(0)2752 4355 y Fk(n)22 b Fo(\015)5 b Fp(\()p Fo(I)2961 4370 y Fj(0)3001 4355 y Fp(\))o(\);)457 4557 y Fo(\015)g Fp(\()p Fo(I)594 4572 y Fj(0)633 4557 y Fp(\))28 b(=)f Fk(f)p Fp(\()p Fo(k)s Fp(\()p Fo(E)6 b Fp(\))p Fo(!)t Fp(\()o Fo(E)g Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))28 b Fk(j)f Fo(E)34 b Fk(2)28 b Fo(I)1925 4572 y Fj(0)1964 4557 y Fk(g)p Fo(:)3174 4431 y Fp(\(1.9\))386 4721 y(\(Here)h Fo(a)701 4685 y Fm(w)786 4721 y Fp(signi\014es)h(W)-8 b(eyl)29 b(quan)m(tization,)i(and)d(1)2210 4736 y Fm(I)2241 4745 y Fh(0)2308 4721 y Fp(is)h(the)f(c)m(haracteristic)j(func-)386 4838 y(tion)h(of)h Fo(I)741 4853 y Fj(0)780 4838 y Fp(.\))486 4954 y(Notice)g(that)f(b)m(y)j(\(1.8\))o(,)e(at)f(least)h(in)m(tuitiv)m (ely)-8 b(,)35 b(for)e(all)f(suc)m(h)i(sym)m(b)s(ols)g Fo(a)1146 5029 y Fi(\015)1146 5089 y(\015)1202 5114 y Fo(a)1253 5073 y Fm(w)1310 5033 y Fi(\000)1355 5114 y Fo(t)1390 5073 y Fn(\000)p Fj(1)1485 5114 y Fo(x;)17 b(p)1633 5033 y Fi(\001)1679 5114 y Fo( )t Fp(\()o Fo(t)p Fp(\))1857 5029 y Fi(\015)1857 5089 y(\015)1940 5114 y Fk(!)27 b Fp(0)32 b(for)g Fo(t)c Fk(!)f(1)p Fo(;)511 b Fp(\(1.10\))386 5274 y(so)33 b(that)f(\(1.9\))g(app)s(ears)h(as)g(a)f (w)m(eak)i(additonal)f(assumption.)486 5390 y(The)43 b(states)g Fo( )k Fp(ob)s(eying)c(the)g(ab)s(o)m(v)m(e)g(conditions)h (\(with)f(\014xed)h Fo(I)2966 5405 y Fj(0)3005 5390 y Fp(\))f(form)f(a)386 5506 y(subspace)34 b(whose)g(closure,)g(sa)m(y)g Fk(H)1687 5521 y Fj(0)1726 5506 y Fp(,)f(is)g Fo(H)8 b Fp({reducing.)486 5623 y(W)-8 b(e)33 b(sho)m(w)g(the)g(follo)m(wing)g (\(main\))g(result.)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 386 259 a Fl(4)793 b(IRA)24 b(HERBST)i(AND)e (ERIK)h(SKIBSTED)386 459 y FC(Theorem)43 b(1.1.)i Fg(Supp)-5 b(ose)38 b Fo(B)5 b Fp(\()p Fo(E)1649 474 y Fj(0)1689 459 y Fp(\))39 b Fg(has)g(an)f(eigenvalue)g(with)i(a)f(p)-5 b(ositive)38 b(r)-5 b(e)g(al)386 575 y(p)g(art.)44 b(Then)33 b(under)h(a)f(c)-5 b(ertain)34 b(assumption)e(c)-5 b(onc)g(erning)33 b(p)-5 b(ossible)32 b(r)-5 b(esonanc)g(es)386 691 y(\(and)24 b(other)h(te)-5 b(chnic)g(al)25 b(c)-5 b(onditions,)25 b(se)-5 b(e)33 b Fp(\(H1\){\(H8\))24 b Fg(in)h(Se)-5 b(ction)24 b(2\))h(ther)-5 b(e)25 b(exists)386 807 y(a)35 b(su\016ciently)g(smal)5 b(l)34 b(op)-5 b(en)34 b(neighb)-5 b(orho)g(o)g(d)33 b Fo(I)2073 822 y Fj(0)2147 807 y Fg(of)i Fo(E)2334 822 y Fj(0)2408 807 y Fg(such)g(that)1679 990 y Fk(H)1763 1005 y Fj(0)1830 990 y Fp(=)28 b Fk(f)o Fp(0)p Fk(g)1043 b Fp(\(1.11\))486 1179 y(A)41 b(sym)m(b)s(ol)i(satisfying)g (the)g(conditions)f(\(1.3\))g(and)g(\(1.4\))f(w)m(as)i(studied)g(b)m(y) 386 1295 y(Guillemin)c(and)f(Sc)m(hae\013er)h([GS].)f(In)g(their)g(pap) s(er)g(the)g(roles)h(of)e Fo(x)h Fp(and)g Fo(\030)43 b Fp(are)386 1411 y(rev)m(ersed)36 b(and)e(their)g Fo(h)g Fp(is)g(homogeneous)g(of)g(degree)g(one)g(in)g Fo(\030)5 b Fp(.)46 b(There)35 b(is)f(only)386 1528 y(one)g(half-line)g(of)g(p)s (oin)m(ts)g(in)g(question)i(rather)e(than)g(a)f(one)i(parameter)f (family)386 1644 y(of)j(half-lines)h(\(their)g(critical)g(set)g(of)f(p) s(oin)m(ts)h(is)g(at)f(zero)h(energy\).)59 b(Under)38 b(the)386 1760 y(condition)29 b(of)g(no)g(resonances)h(they)g(obtain)f (a)g(conjugation)f(of)h Fo(H)36 b Fp(to)29 b(a)f(simpler)386 1876 y(normal)38 b(form)f(from)h(whic)m(h)h(they)g(dra)m(w)g (conclusions)g(ab)s(out)f(propagation)f(of)386 1993 y(singularities)d (for)e(an)g(equation)i(of)e(the)h(form)f Fo(H)8 b( )31 b Fp(=)d Fo(\036)p Fp(.)486 2109 y(T)-8 b(o)36 b(see)i(what)f(our)g (result)g(means)h(in)f(a)f(particular)h(mo)s(del,)h(namely)g(in)f(the) 386 2225 y(case)25 b(where)g Fo(h)e Fp(is)i(giv)m(en)g(b)m(y)f Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h(2)1857 2189 y Fn(\000)p Fj(1)1951 2225 y Fo(\030)1999 2189 y Fj(2)2042 2225 y Fp(+)t Fo(V)22 b Fp(\()5 b(^)-55 b Fo(x)q Fp(\))24 b(with)g Fo(V)45 b Fp(a)24 b(Morse)g(function)386 2341 y(on)e Fo(S)577 2305 y Fm(n)p Fn(\000)p Fj(1)714 2341 y Fp(,)j(w)m(e)f(recall)f(from)f([H]:)h(The)h(sp)s(ectrum)g(of)e Fo(H)35 b Fp(=)28 b(2)2524 2305 y Fn(\000)p Fj(1)2618 2341 y Fo(p)2667 2305 y Fj(2)2708 2341 y Fp(+)r Fo(V)21 b Fp(\()6 b(^)-55 b Fo(x)q Fp(\))22 b(is)h(purely)386 2458 y(absolutely)34 b(con)m(tin)m(uous)g(and)1629 2656 y Fo(I)i Fp(=)1833 2562 y Fi(X)1812 2773 y Fm(!)1856 2785 y Ff(l)1880 2773 y Fn(2C)1964 2781 y Ff(r)2015 2656 y Fo(P)2078 2671 y Fm(l)2104 2656 y Fo(;)994 b Fp(\(1.12\))386 2939 y(where)50 b Fo(P)747 2954 y Fm(l)822 2939 y Fp(are)e Fo(H)8 b Fp({reducing)50 b(orthogonal)e(pro)5 b(jections)50 b(de\014ned)g(as)f(follo)m(ws:)386 3055 y(Pic)m(k)23 b(an)m(y)g(family)f Fk(f)p Fo(\037)1165 3070 y Fm(l)1191 3055 y Fk(j)p Fo(!)1280 3070 y Fm(l)1333 3055 y Fk(2)28 b Fo(C)1497 3070 y Fm(r)1535 3055 y Fk(g)21 b Fp(of)g(smo)s(oth)h (functions)h(on)f Fo(S)2641 3019 y Fm(n)p Fn(\000)p Fj(1)2799 3055 y Fp(with)h Fo(\037)3072 3070 y Fm(k)3114 3055 y Fp(\()p Fo(!)3213 3070 y Fm(l)3239 3055 y Fp(\))28 b(=)386 3171 y Fo(\016)429 3186 y Fm(k)r(l)527 3171 y Fp(\(the)33 b(Kronec)m(k)m(er)i(sym)m(b)s(ol\);)f(here)g Fo(C)1878 3186 y Fm(r)1949 3171 y Fp(is)f(the)h(\014nite)g(set)f(of)g (non-degenerate)386 3287 y(critical)g(p)s(oin)m(ts)g(in)g Fo(S)1184 3251 y Fm(n)p Fn(\000)p Fj(1)1354 3287 y Fp(for)f Fo(V)21 b Fp(.)44 b(Then)1283 3470 y Fo(P)1346 3485 y Fm(l)1399 3470 y Fp(=)28 b Fo(s)22 b Fk(\000)38 b Fp(lim)1670 3530 y Fm(t)p Fn(!1)1854 3470 y Fo(e)1899 3429 y Fm(itH)2016 3470 y Fo(\037)2077 3485 y Fm(l)2103 3470 y Fp(\()6 b(^)-55 b Fo(x)p Fp(\))p Fo(e)2279 3429 y Fn(\000)p Fm(itH)2451 3470 y Fo(;)386 3689 y Fp(see)35 b([H])f(and)h([A)m(CH].)g(F)-8 b(urthermore)34 b(in)h([H])f(the)g(existence)j(of)c(an)h(asymptotic)386 3805 y(momen)m(tum)28 b Fo(p)941 3769 y Fj(+)1027 3805 y Fp(w)m(as)f(pro)m(v)m(ed)i(and)d(its)i(relationship)f(to)g(the)g(ab)s (o)m(v)m(e)g(pro)5 b(jections)386 3921 y(w)m(as)35 b(sho)m(wn.)48 b(See)35 b(also)e([HS2].)48 b(\(There)35 b(w)m(as)f(the)h(restriction)f (in)g([H])g(to)g Fo(n)c Fk(\025)g Fp(3)386 4038 y(but)35 b(this)h(is)g(easily)h(remo)m(v)m(ed)g(using)f(the)g(Mourre)f(estimate) i([A)m(CH,)f(Theorem)386 4154 y(C.1].\))486 4270 y(W)-8 b(e)35 b(notice)g(that)f(\(1.12\))g(has)h(an)g(analogue)f(in)h (Classical)i(Mec)m(hanics:)50 b(An)m(y)386 4386 y(classical)f(orbit)f (\(except)i(for)e(the)g(exceptional)i(ones)f(that)e(collapse)j(at)d (the)386 4503 y(origin\))32 b(ob)s(eys)i Fk(j)p Fo(x)p Fk(j)27 b(!)h(1)k Fp(with)39 b(^)-55 b Fo(x)28 b Fk(!)f Fo(!)1863 4518 y Fm(l)1922 4503 y Fp(for)32 b(some)h Fo(!)2376 4518 y Fm(l)2429 4503 y Fk(2)28 b Fo(C)2593 4518 y Fm(r)2631 4503 y Fp(.)486 4619 y(Ob)m(viously)23 b(the)f(collection)h(\(1.2\){\(1.4\))e(corresp)s(onds)i(in)f(the)g(p)s (oten)m(tial)g(mo)s(del)386 4767 y(exactly)41 b(to)d Fo(C)924 4782 y Fm(r)962 4767 y Fp(:)57 b(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))39 b(=)1739 4656 y Fi(\020)1799 4767 y Fo(!)1860 4782 y Fm(l)1885 4767 y Fo(;)1929 4681 y Fi(p)p 2029 4681 566 4 v 86 x Fp(2\()o Fo(E)29 b Fk(\000)22 b Fo(V)g Fp(\()p Fo(!)2493 4782 y Fm(l)2518 4767 y Fp(\)\))p Fo(!)2655 4782 y Fm(l)2681 4656 y Fi(\021)2780 4767 y Fp(with)40 b Fo(!)3070 4782 y Fm(l)3134 4767 y Fk(2)g Fo(C)3310 4782 y Fm(r)3348 4767 y Fp(.)386 4909 y(The)k(assumption)g(that)f(the)g (real)g(part)g(of)g(one)g(eigen)m(v)-5 b(alue)44 b(is)g(p)s(ositiv)m(e) g(cor-)386 5025 y(resp)s(onds)39 b(to)f Fo(!)982 5040 y Fm(l)1045 5025 y Fp(b)s(eing)g(either)h(a)f(lo)s(cal)f(maxim)m(um)j (or)d(a)h(saddle)h(p)s(oin)m(t)f(of)f Fo(V)22 b Fp(.)386 5141 y(Moreo)m(v)m(er)34 b(w)m(e)g(ha)m(v)m(e)g(the)f(iden)m (ti\014cation)1420 5324 y Fk(H)1504 5339 y Fj(0)1571 5324 y Fp(=)28 b(Ran)16 b(\()p Fo(P)1967 5339 y Fm(l)1993 5324 y Fp(1)2042 5339 y Fm(I)2073 5348 y Fh(0)2111 5324 y Fp(\()p Fo(H)8 b Fp(\)\))o Fo(:)785 b Fp(\(1.13\))386 5506 y(Whence,)52 b(up)s(on)46 b(v)-5 b(arying)47 b Fo(I)1466 5521 y Fj(0)1506 5506 y Fp(,)j(Theorem)e(1.1)e(yields)i(the)f(follo)m (wing)g(for)f(the)386 5623 y(p)s(oten)m(tial)33 b(mo)s(del.)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)809 b(5)386 459 y FC(Theorem)37 b(1.2.)k Fg(Supp)-5 b(ose)33 b Fo(!)1506 474 y Fm(l)1559 459 y Fk(2)28 b Fo(C)1723 474 y Fm(r)1795 459 y Fg(is)33 b(the)h(lo)-5 b(c)g(ation)33 b(of)g(a)h(lo)-5 b(c)g(al)33 b(maximum)g(or)386 575 y(a)i(sadd)5 b(le)33 b(p)-5 b(oint)35 b(of)g Fo(V)21 b Fg(.)45 b(Then)1732 699 y Fo(P)1795 714 y Fm(l)1849 699 y Fp(=)27 b(0)p Fo(:)1097 b Fp(\(1.14\))486 878 y(A)27 b(detailed)g(analysis)i(of)d(the)i(large)f(time)g(asymptotic)h(b)s(eha) m(vior)g(of)f(states)g(in)386 994 y(the)35 b(range)f(of)g(the)h(pro)5 b(jections)36 b Fo(P)1673 1009 y Fm(l)1733 994 y Fp(whic)m(h)g(corresp) s(ond)f(to)f(lo)s(cal)h(minima)g(w)m(as)386 1110 y(accomplished)j (recen)m(tly)h(in)e([HS2].)55 b(In)37 b(particular)g(for)e(an)m(y)j(lo) s(cal)e(minim)m(um,)386 1226 y Fo(P)449 1241 y Fm(l)502 1226 y Fk(6)p Fp(=)28 b(0.)42 b(Moreo)m(v)m(er)30 b(in)f(this)g(case)g (w)m(e)h(ha)m(v)m(e)g(\(1.13\))d(for)h(the)h(analogous)g(space)g(of)386 1343 y(that)34 b(in)g(Theorem)h(1.1.)48 b(One)34 b(ma)m(y)h(easily)g (include)h(in)e(Theorem)h(1.2)f(a)g(short-)386 1459 y(range)g(p)s (erturbation)h Fo(V)1284 1474 y Fj(1)1355 1459 y Fp(=)c Fo(O)1540 1378 y Fi(\000)1584 1459 y Fk(j)p Fo(x)p Fk(j)1695 1423 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\016)1878 1378 y Fi(\001)1924 1459 y Fp(,)k Fo(\016)g(>)c Fp(0,)k Fo(@)2338 1423 y Fm(\013)2333 1483 y(x)2388 1459 y Fo(V)2445 1474 y Fj(1)2516 1459 y Fp(=)30 b Fo(O)s Fp(\()p Fk(j)p Fo(x)p Fk(j)2849 1423 y Fn(\000)p Fj(2)2943 1459 y Fp(\),)35 b Fk(j)p Fo(\013)q Fk(j)30 b Fp(=)h(2,)386 1577 y(to)h(the)h (Hamiltonian)g Fo(H)8 b Fp(,)32 b(see)i(Remarks)f(8.3)g(\(1\).)486 1693 y(The)f(result)g(Theorem)g(1.1)f(is)h(m)m(uc)m(h)h(more)e(general) h(than)f(Theorem)i(1.2.)42 b(In)386 1809 y(particular,)h(as)f(a)e (further)i(application,)h(w)m(e)f(can)f(apply)h(it)f(to)g(a)f(problem)i (of)386 1925 y(a)g(quan)m(tum)h(particle)g(in)f(t)m(w)m(o)h(dimensions) h(sub)5 b(ject)44 b(to)d(an)h(electromagnetic)386 2042 y(p)s(oten)m(tial)30 b(whic)m(h)h(is)f(asymptotically)i(homogeneous)f (of)e(degree)i(zero)f(in)g Fo(x)p Fp(,)h(see)386 2158 y([CHS2].)44 b(\(F)-8 b(or)29 b(another)i(magnetic)h(\014eld)f(problem) h(in)f(this)g(class)h(see)g([CHS1].\))386 2274 y(Let)h(us)g(also)g(giv) m(e)g(a)f(simple)i(example)g(from)f(Riemannian)g(geometry)-8 b(.)386 2453 y Fg(Example)41 b Fp(1.3)p Fg(.)g Fp(Consider)34 b(the)f(sym)m(b)s(ol)h Fo(h)f Fp(on)f(\()p FC(R)2239 2417 y Fj(2)2300 2453 y Fk(n)22 b(f)p Fp(0)p Fk(g)p Fp(\))g Fk(\002)g FC(R)2764 2417 y Fj(2)724 2666 y Fo(h)28 b Fp(=)f Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1331 2599 y(1)p 1331 2643 49 4 v 1331 2734 a(2)1390 2585 y Fi(\000)1435 2666 y Fp(1)22 b(+)g Fo(ax)1710 2625 y Fj(2)1710 2691 y(2)1750 2666 y Fk(j)p Fo(x)p Fk(j)1861 2625 y Fn(\000)p Fj(2)1955 2585 y Fi(\001)2001 2608 y Fn(\000)p Fj(1)2095 2666 y Fo(\030)2143 2625 y Fj(2)2138 2691 y(1)2204 2666 y Fp(+)2312 2599 y(1)p 2312 2643 V 2312 2734 a(2)2371 2666 y Fo(\030)2419 2625 y Fj(2)2414 2691 y(2)2458 2666 y Fp(;)44 b Fo(a)28 b(>)g Fp(0)p Fo(:)337 b Fp(\(1.15\))386 2883 y(The)29 b(family)f(\(1)p Fo(;)17 b Fp(0;)1099 2799 y Fk(p)p 1181 2799 127 4 v 1181 2883 a Fp(2)p Fo(E)6 b(;)17 b Fp(0\),)28 b Fo(E)34 b(>)28 b Fp(0,)g(consists)i(of)d(p)s(oin) m(ts)i(ob)s(eying)h(\(1.2\))o(,)f(\(1.3\))386 3000 y(and)g(\(1.4\).)42 b(F)-8 b(or)29 b(the)h(linearized)g(reduced)h(\015o)m(w)h(\(1.7\))d(w)m (e)h(\014nd)g(the)g(eigen)m(v)-5 b(alues)396 3080 y Fj(1)p 396 3096 36 4 v 396 3154 a(2)441 3119 y Fp(\()p Fk(\000)p Fp(1)13 b Fk(\000)708 3041 y(p)p 792 3041 269 4 v 792 3119 a Fp(1)22 b(+)g(4)p Fo(a)p Fp(\))28 b(and)1322 3080 y Fj(1)p 1322 3096 36 4 v 1322 3154 a(2)1368 3119 y Fp(\()p Fk(\000)p Fp(1)13 b(+)1634 3041 y Fk(p)p 1717 3041 269 4 v 78 x Fp(1)22 b(+)g(4)p Fo(a)p Fp(\),)29 b(and)f(w)m(e)h(conclude)h (that)e(the)g(\014xed)386 3236 y(p)s(oin)m(ts)39 b(are)g(saddle)h(p)s (oin)m(ts.)62 b(If)39 b Fo(a)g Fp(is)g(irrational)g(there)g(are)g(no)g (resonances)h(of)386 3352 y(an)m(y)48 b(order)f(\(see)h(Section)h(2)d (for)h(de\014nition\),)52 b(whence)d(w)m(e)f(ma)m(y)g(infer)g(from)386 3468 y(Theorem)28 b(1.1)f(that)g(there)h(is)g(no)f(quan)m(tum)i(c)m (hannel)f(asso)s(ciated)h(to)d(the)i(family)386 3584 y(of)33 b(\014xed)h(p)s(oin)m(ts)f(in)h(this)g(case.)45 b(Using)34 b(the)g(absence)g(of)f(lo)m(w)h(order)f(resonances)386 3700 y(condition)j(\(2.6\))e(w)m(e)i(ma)m(y)g(in)f(fact)g(obtain)g (this)h(conclusion)g(for)f Fo(a)d Fk(6)p Fp(=)3048 3661 y Fj(3)p 3048 3678 36 4 v 3048 3735 a(4)3094 3700 y Fo(;)17 b Fp(2;)36 b(see)386 3817 y(Remark)31 b(2.1)e(for)h(a)g(further)g (discussion.)45 b(W)-8 b(e)30 b(ha)m(v)m(e)i(tacitly)f(assumed)g(that)f (the)386 3933 y(sym)m(b)s(ol)k(\(1.15\))e(is)h(suitably)g(regularized)h (at)e Fo(x)c Fp(=)g(0)k(\(for)g(the)h(quan)m(tization\).)486 4112 y(Our)f(pro)s(of)g(of)g(Theorem)i(1.1)e(consists)i(of)e(three)i (parts:)486 4228 y(I\))c(Assuming)i Fo( )t Fp(\()o Fo(t)p Fp(\))c(=)g Fo(e)1389 4192 y Fn(\000)p Fm(itH)1561 4228 y Fo( )34 b Fp(do)s(es)c(lo)s(calize)h(in)g(phase)g(space)g(as)f Fo(t)e Fk(!)g(1)h Fp(in)386 4344 y(the)j(region)h Fk(j)p Fo(u)p Fk(j)20 b Fp(+)h Fk(j)p Fo(\021)t Fk(j)26 b(\024)j Fo(\017)j Fp(for)f(an)m(y)i Fo(\017)28 b(>)g Fp(0,)k(w)m(e)h(pro)m(v)m (e)g(a)f(stronger)h(lo)s(calization.)386 4460 y(Namely)-8 b(,)32 b(for)d(some)i(small)g(p)s(ositiv)m(e)h Fo(\016)t Fp(,)f(the)f(probabilit)m(y)h(\(assuming)h(here)f(that)386 4577 y Fo( )i Fp(is)d(normalized\))g(that)f Fo( )t Fp(\()p Fo(t)p Fp(\))g(is)h(lo)s(calized)f(in)h(the)f(region)h Fk(j)p Fo(u)p Fk(j)15 b Fp(+)g Fk(j)p Fo(\021)t Fk(j)25 b(\025)k Fo(t)3071 4540 y Fn(\000)p Fm(\016)3193 4577 y Fp(go)s(es)386 4693 y(to)j(zero)h(as)g Fo(t)28 b Fk(!)f(1)32 b Fp(.)486 4809 y(I)s(I\))45 b(Using)h(I\))g(and)g(an)f(iteration)h(sc) m(heme,)51 b(w)m(e)c(construct)g(an)e(observ)-5 b(able)386 4925 y(\000)41 b(whic)m(h)j(decreases)g(\\rapidly")e(to)f(zero.)71 b(This)43 b(iteration)f(sc)m(heme)i(is)e(based)386 5042 y(on)d(one)h(used)h(b)m(y)g(P)m(oincar)m(\023)-46 b(e)40 b(\(see)h([A1,)h(pp.)65 b(177{180]\))38 b(to)h(obtain)g(a)h(c)m(hange) 386 5158 y(of)f(co)s(ordinates)g(whic)m(h)i(linearizes)g(\(1.6\).)63 b(The)40 b(fact)f(that)h(if)f(one)g(eigen)m(v)-5 b(alue)386 5274 y(of)40 b Fo(B)5 b Fp(\()p Fo(E)h Fp(\))40 b(has)g(a)g(p)s(ositiv) m(e)i(real)e(part)g(then)h(another)f(has)h(real)f(part)g Fo(<)h Fk(\000)p Fp(1)f(is)386 5390 y(relev)-5 b(an)m(t)45 b(here.)78 b(Our)44 b(observ)-5 b(able)45 b(\000)e(is)i(in)f(\014rst)g (appro)m(ximation)h(roughly)f(a)386 5506 y(quan)m(tization)g(of)e(a)g (comp)s(onen)m(t)i(of)e Fo(w)j Fp(in)e(\(1.7\))f(whic)m(h)i(deca)m(ys)h (as)e(exp)17 b(\()p Fo(\025\034)11 b Fp(\))386 5623 y(with)33 b(Re)17 b Fo(\025)27 b(<)h Fk(\000)p Fp(1.)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 386 259 a Fl(6)793 b(IRA)24 b(HERBST)i(AND)e (ERIK)h(SKIBSTED)486 459 y Fp(I)s(I)s(I\))37 b(Using)g(Mourre)h(theory) g(w)m(e)g(pro)m(v)m(e)g(an)f(uncertain)m(t)m(y)i(principle)g(lemma)386 575 y(for)31 b(t)m(w)m(o)h(self-adjoin)m(t)f(op)s(erators)g Fo(P)45 b Fp(and)31 b Fo(Q)g Fp(satisfying)i Fo(i)p Fp([)p Fo(P)s(;)17 b(Q)p Fp(])27 b Fk(\025)i Fo(cI)8 b(;)114 b(c)27 b(>)h Fp(0,)386 691 y(and)37 b(some)g(tec)m(hnical)h (conditions.)57 b(The)37 b(lemma)h(states)f(that)f(if)h Fo(\016)2914 706 y Fj(1)2988 691 y Fo(<)d(\016)3141 706 y Fj(2)3218 691 y Fp(and)386 807 y Fo(g)433 822 y Fj(1)505 807 y Fp(and)e Fo(g)741 822 y Fj(2)813 807 y Fp(are)h(t)m(w)m(o)g(b)s (ounded)g(compactly)h(supp)s(orted)f(functions)h(then)1258 965 y(lim)1243 1025 y Fm(t)p Fn(!1)1426 880 y Fi(\015)1426 940 y(\015)1481 965 y Fo(g)1528 980 y Fj(1)1568 884 y Fi(\000)1613 965 y Fo(t)1648 924 y Fn(\000)p Fm(\016)1734 933 y Fh(1)1773 965 y Fo(Q)1850 884 y Fi(\001)1896 965 y Fo(g)1943 980 y Fj(2)1982 884 y Fi(\000)2028 965 y Fo(t)2063 924 y Fm(\016)2094 933 y Fh(2)2133 965 y Fo(P)2210 884 y Fi(\001)2255 880 y(\015)2255 940 y(\015)2338 965 y Fp(=)28 b(0)p Fo(:)386 1159 y Fp(If)38 b Fo( )k Fp(is)c(normalized)h (this)f(b)s(ound)g(implies)i(that)e(the)g(lo)s(calizations)g(of)g(I\))g (and)386 1275 y(I)s(I\))32 b(are)h(incompatible.)486 1392 y(The)g(basic)h(theme)g(of)f(our)f(pap)s(er)h(ma)m(y)h(b)s(e)f (phrased)h(as)f(absence)i(of)d(certain)386 1508 y(quan)m(tum)25 b(mec)m(hanical)g(states)f(whic)m(h)i(are)d(presen)m(t)i(in)f(the)g (corresp)s(onding)g(clas-)386 1624 y(sical)39 b(mo)s(del.)62 b(Notice)39 b(that)g(giv)m(en)g(an)m(y)h(critical)f(p)s(oin)m(t)f Fo(!)2588 1639 y Fm(l)2652 1624 y Fk(2)g Fo(C)2826 1639 y Fm(r)2903 1624 y Fp(\(restricting)386 1740 y(for)29 b(con)m(v)m(enience)j(the)e(discussion)h(to)e(the)g(p)s(oten)m(tial)h (mo)s(del\))f(there)h(are)f(indeed)386 1857 y(classical)j(orbits)e (with)h Fk(j)p Fo(x)p Fk(j)d(!)f(1)j Fp(and)37 b(^)-55 b Fo(x)28 b Fk(!)f Fo(!)2108 1872 y Fm(l)2134 1857 y Fp(;)k(in)f(particular)h(this)g(is)g(the)g(case)386 1973 y(for)e(an)m(y)i(giv)m(en)g(lo)s(cal)e(maxim)m(um)j(or)d(saddle)i(p)s (oin)m(t.)43 b(In)m(tuitiv)m(ely)-8 b(,)33 b(Theorem)e(1.1)386 2089 y(is)39 b(true)g(b)s(ecause)h(the)f(asso)s(ciated)h(classical)g (orbits)f(o)s(ccur)g(for)f(only)h(a)f(\\rare")386 2205 y(set)i(of)e(initial)h(conditions)h(as)f(\014xed)h(b)m(y)g(the)f (stable)h(manifold)f(theorem.)63 b(Al-)386 2321 y(ternativ)m(ely)-8 b(,)40 b(for)d(some)h(comp)s(onen)m(ts)h(of)e(\()6 b(^)-55 b Fo(x;)17 b(\030)5 b Fp(\))36 b(the)i(con)m(v)m(ergence)i(to)d(\()p Fo(!)3161 2336 y Fm(l)3187 2321 y Fo(;)17 b(\030)3279 2285 y Fj(+)3337 2321 y Fp(\))386 2438 y(is)44 b(\\to)s(o)f(fast")h(th) m(us)g(b)s(eing)h(incompatible)g(with)f(the)g(uncertain)m(t)m(y)i (principle)386 2554 y(in)34 b(Quan)m(tum)g(Mec)m(hanics.)49 b(These)35 b(t)m(w)m(o)f(di\013eren)m(t)h(explanations)f(are)g (actually)386 2670 y(connected.)486 2786 y(F)-8 b(or)31 b(another)i(example)h(of)e(this)h(theme)h(w)m(e)g(refer)f(to)f([G2],)g ([S1])h(and)f([S2].)486 2903 y(W)-8 b(e)27 b(addressed)i(the)f(problem) g(of)f(Theorem)h(1.2)f(in)g(a)g(previous)i(w)m(ork,)g([HS1],)386 3019 y(where)24 b(w)m(e)g(pro)m(v)m(ed)h(\(1.14\))d(at)h(lo)s(cal)g (maxima)h(but)f(only)h(had)f(a)g(partial)g(result)h(for)386 3135 y(saddle)36 b(p)s(oin)m(ts)f(\(using)g(a)f(di\013eren)m(t)i(metho) s(d\).)50 b(In)34 b(the)h(t)m(w)m(o-dimensional)i(case)386 3251 y(with)f(homogeneous)g(p)s(oten)m(tial)f(a)g(related)g(result)h (concerning)h(distributional)386 3368 y(eigenfunctions)d(w)m(as)g(pro)m (v)m(ed)g(in)f([HMV].)386 3543 y(1.1.)48 b FC(A)j(generalization.)f Fp(Before)44 b(getting)g(in)m(to)h(the)f(details)h(of)f(the)h(pro)s(of) 386 3660 y(of)d(Theorems)h(1.1)f(and)g(1.2,)i(w)m(e)g(consider)f(p)s (ossible)g(generalizations)h(of)d(the)386 3776 y(homogeneit)m(y)35 b(condition)e Fo(x)23 b Fk(\001)g(r)1596 3791 y Fm(x)1639 3776 y Fo(h)p Fp(\()q Fo(x;)17 b(\030)5 b Fp(\))28 b(=)g(0.)45 b(W)-8 b(e)34 b(will)g(fo)s(cus)f(our)g(discussion)386 3892 y(on)h(the)h(structure)g(of)f(the)g(classical)i(mec)m(hanics)g(of) e(our)g(mo)s(dels)h(and)f(lea)m(v)m(e)i(to)386 4008 y(the)d(reader)g(a) f(form)m(ulation)h(of)f(the)h(quan)m(tum)h(problem.)486 4124 y(The)j(ab)s(o)m(v)m(e)h(homogeneit)m(y)h(condition)e(is)g(b)s (est)h(understo)s(o)s(d)f(as)g(the)h(in)m(v)-5 b(ari-)386 4241 y(ance)39 b(of)e(the)h(Hamiltonian)h(under)g(the)f(\015o)m(w)h (generated)f(b)m(y)h(the)g(v)m(ector)g(\014eld)386 4357 y Fo(v)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)790 4282 y Fi(P)912 4357 y Fo(x)967 4372 y Fm(i)996 4357 y Fo(@)5 b(=@)g(x)1212 4372 y Fm(i)1242 4357 y Fp(,)33 b(or)f(in\014nitesimally)1612 4515 y Fo(v)t(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h(0)p Fo(:)976 b Fp(\(1.16\))386 4672 y(Our)32 b(goal)g(is)h(th)m(us)h(to)e(\014nd)h(in)m(v)-5 b(ariance)34 b(conditions)g(\(1.16\))d(whic)m(h)k(will)534 4809 y(\(a\))41 b(reduce)47 b(the)e(dimension)i(of)e(phase)h(space)g(b) m(y)g(t)m(w)m(o)g(giving)f(an)h(auto-)700 4925 y(nomous)j(dynamical)g (system)g(in)f(dimension)h(2)p Fo(n)33 b Fk(\000)g Fp(2)47 b(\(usually)i(not)700 5042 y(Hamiltonian\))529 5158 y(\(b\))41 b(giv)m(e)29 b(a)d(natural)h(framew)m(ork)i(for)d(discussing)k (stabilit)m(y)e(of)f(orbits)g(whic)m(h)700 5274 y(do)i(not)g(lie)g(in)g (a)g(compact)g(set.)43 b(It)29 b(will)g(turn)g(out)g(that)f(stabilit)m (y)j(is)e(not)700 5390 y(measured)39 b(using)f(an)m(y)g(preexisting)g (metric)g(in)g(the)f(phase)h(space)g(but)700 5506 y(rather)c(using)f (bundles)i(of)d(orbits)i(of)e(the)h(v)m(ector)h(\014eld)g Fo(v)j Fp(surrounding)700 5623 y(a)c(giv)m(en)g(orbit)g(of)f(the)h (Hamiltonian)g(v)m(ector)h(\014eld,)f Fo(v)2693 5638 y Fm(h)2738 5623 y Fp(.)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)809 b(7)486 459 y Fp(The)31 b(v)m(ector)h(\014eld)f Fo(v)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1588 384 y Fi(P)1710 459 y Fo(x)1765 474 y Fm(i)1794 459 y Fo(@)5 b(=@)g(x)2010 474 y Fm(i)2070 459 y Fp(do)s(es)31 b(not)g(generate)g(a)f(symplectic)386 575 y(\015o)m(w)40 b(but)g(do)s(es)g(satisfy)g(a)g(crucial)g(prop)s(ert)m(y)-8 b(.)65 b(Namely)41 b Fk(L)2613 590 y Fm(v)2653 575 y Fo(!)i Fp(=)d Fo(!)i Fp(where)f Fk(L)3334 590 y Fm(v)386 691 y Fp(is)h(the)g(Lie)g(deriv)-5 b(ativ)m(e)43 b(in)f(direction)g Fo(v)j Fp(and)d Fo(!)i Fp(is)e(the)g(symplectic)j(form.)70 b(It)386 807 y(will)34 b(turn)g(out)g(\(see)g(Lemma)h(1.4\))e(that)g(a) g(geometric)i(condition)f(suc)m(h)h(as)f(this)386 924 y(\(although)40 b(more)g(restrictiv)m(e)i(than)e(necessary\))j(will)d (guaran)m(tee)h(that)f Fo(v)j Fp(is)e(a)386 1040 y(suitable)34 b(v)m(ector)f(\014eld.)486 1156 y(W)-8 b(e)36 b(will)h(require)h Fo(v)i Fp(to)c(satisfy)i(certain)f(conditions)g(relativ)m(e)h(to)e Fo(v)3016 1171 y Fm(h)3061 1156 y Fp(,)h(where)386 1272 y Fo(v)433 1287 y Fm(h)512 1272 y Fp(is)d(a)g(Hamiltonian)g(v)m(ector)h (\014eld)f(on)g(a)g(symplectic)i(manifold)e(\()p Fo(M)5 b(;)17 b(!)t Fp(\))33 b(with)386 1389 y(Hamiltonian)g Fo(h)p Fp(:)534 1533 y(\(1\))41 b(In)34 b(a)g(neigh)m(b)s(orho)s(o)s(d) f(of)g(a)h(p)s(oin)m(t)f Fo(x)2024 1548 y Fj(0)2094 1533 y Fk(2)d Fo(M)10 b Fp(,)34 b(the)g(lo)s(cal)g(\015o)m(w)g Fo(\036)3018 1497 y Fm(v)3018 1558 y(t)3059 1533 y Fp(\()p Fk(\001)p Fp(\))f(gen-)700 1649 y(erated)i(b)m(y)g Fo(v)j Fp(exists)e(for)d(all)h Fo(t)c Fk(2)h Fp(\()p Fk(\000)p Fo(\017;)17 b Fk(1)p Fp(\))34 b(for)g(some)g Fo(\017)d(>)f Fp(0)k(and)g(there)700 1765 y(exists)39 b(a)d(surface)h Fo(S)42 b Fp(con)m(taining)37 b Fo(x)2026 1780 y Fj(0)2066 1765 y Fp(,)g(transv)m(erse)h(to)e Fo(v)t Fp(,)h(and)g(a)f(di\013eo-) 700 1882 y(morphism)31 b Fo(\033)h Fp(:)c Fo(B)33 b Fk(!)27 b Fo(S)6 b Fp(,)30 b(where)h Fo(B)k Fp(is)30 b(a)g(ball)g(in)g FC(R)2596 1845 y Fj(2)p Fm(n)p Fn(\000)p Fj(1)2798 1882 y Fp(cen)m(tered)h(at)f(0,)700 1998 y(suc)m(h)35 b(that)d(the)h(map) 1169 2170 y Fo(B)27 b Fk(\002)c Fp(\()p Fk(\000)p Fo(\017;)17 b Fk(1)p Fp(\))28 b Fk(3)g Fp(\()p Fo(w)s(;)17 b(t)p Fp(\))27 b Fk(!)g Fo(\036)2268 2129 y Fm(v)2268 2195 y(t)2309 2170 y Fp(\()o Fo(\033)t Fp(\()p Fo(w)s Fp(\)\))700 2343 y(is)35 b(a)e(di\013eomorphism)j(on)m(to)e(its)g(image,)h Fk(K)2315 2358 y Fj(0)2354 2343 y Fp(.)47 b(W)-8 b(e)35 b(also)f(assume)h Fo(v)j Fp(and)700 2459 y Fo(v)747 2474 y Fm(h)824 2459 y Fp(are)33 b(parallel)f(\(and)g(nonzero\))h(along)e (the)i(p)s(ositiv)m(e)g(orbit)f(of)g Fo(v)k Fp(orig-)700 2575 y(inating)d(at)f Fo(x)1205 2590 y Fj(0)1245 2575 y Fp(.)534 2691 y(\(2\))41 b(There)34 b(are)f(smo)s(oth)g(functions)g Fo(\014)38 b Fp(and)33 b Fo(\015)k Fp(suc)m(h)d(that)1360 2864 y([)p Fo(v)t(;)17 b(v)1529 2879 y Fm(h)1574 2864 y Fp(])28 b(=)f Fo(\014)6 b(v)1840 2879 y Fm(h)1907 2864 y Fp(+)22 b Fo(\015)5 b(v)36 b Fp(in)d Fk(K)2334 2879 y Fj(0)2373 2864 y Fo(:)534 3036 y Fp(\(3\))41 b Fo(v)t(h)28 b Fp(=)g(0)k(in)h Fk(K)1210 3051 y Fj(0)1249 3036 y Fp(.)486 3181 y(Condition)43 b(\(1\))f(allo)m(ws)h(us)g(to)f(assume)i(\(after)e (a)g(c)m(hange)h(of)f(co)s(ordinates\))386 3297 y(that)33 b Fk(K)674 3312 y Fj(0)743 3297 y Fp(=)d Fo(B)e Fk(\002)23 b Fp(\()p Fk(\000)p Fo(\017;)17 b Fk(1)p Fp(\),)34 b Fo(x)1503 3312 y Fj(0)1573 3297 y Fp(=)29 b(\(0)p Fo(;)17 b Fp(0\))o(,)34 b(and)g Fo(v)g Fp(=)29 b(\(0)p Fo(;)17 b(:)g(:)g(:)f(;)h Fp(0)p Fo(;)g Fp(1\))32 b(in)i Fk(K)3042 3312 y Fj(0)3081 3297 y Fp(.)47 b(With)386 3413 y(the)33 b(notation)f Fo(x)999 3428 y Fn(?)1086 3413 y Fp(=)c(\()p Fo(x)1283 3428 y Fj(1)1323 3413 y Fo(;)17 b(:)g(:)g(:)e(;)i(x)1596 3428 y Fj(2)p Fm(n)p Fn(\000)p Fj(1)1769 3413 y Fp(\))32 b(for)g Fo(x)d Fk(2)f FC(R)2250 3377 y Fj(2)p Fm(n)2332 3413 y Fp(,)k(condition)h(\(2\))f(implies)1288 3585 y(\()p Fo(v)1373 3600 y Fm(h)1418 3585 y Fp(\))1456 3614 y Fn(?)1515 3585 y Fp(\()p Fo(x)p Fp(\))c(=)f Fo(k)s Fp(\()p Fo(x)p Fp(\))q(\()p Fo(v)2048 3600 y Fm(h)2093 3585 y Fp(\))2131 3614 y Fn(?)2190 3585 y Fp(\()p Fo(x)2283 3600 y Fn(?)2342 3585 y Fo(;)17 b Fp(0\))386 3758 y(for)29 b(some)h(p)s(ositiv)m(e)g Fo(k)s Fp(\()p Fk(\001)p Fp(\))f(so)h(that)f(in)m(tro)s(ducing)h(the)g (new)g(time)g(v)-5 b(ariable)29 b Fo(\034)41 b Fp(with)386 3874 y Fo(d\034)11 b(=dt)27 b Fp(=)h Fo(k)s Fp(\()p Fo(x)p Fp(\()p Fo(t)p Fp(\))q(\))k(the)h(\014rst)g(2)p Fo(n)22 b Fk(\000)h Fp(1)32 b(of)g(Hamilton's)i(equations)f(b)s(ecome)1464 4033 y Fo(dx)1570 4048 y Fn(?)p 1464 4077 166 4 v 1494 4168 a Fo(d\034)1667 4100 y Fp(=)27 b(\()p Fo(v)1855 4115 y Fm(h)1900 4100 y Fp(\))1938 4129 y Fn(?)1997 4100 y Fp(\()p Fo(x)2090 4115 y Fn(?)2149 4100 y Fo(;)17 b Fp(0\))p Fo(:)386 4308 y Fp(As)34 b(long)g(as)g Fo(dh)p Fp(\()p Fo(x)1065 4323 y Fj(0)1105 4308 y Fp(\))c Fk(6)p Fp(=)g(0,)k(using)h(condition)f(\(3\))g(w)m(e)h(can)f(eliminate)h(one)f (more)386 4424 y(v)-5 b(ariable)33 b(using)h(energy)g(conserv)-5 b(ation,)34 b Fo(h)p Fp(\()p Fo(x)p Fp(\))29 b(=)f Fo(h)p Fp(\()p Fo(x)2378 4439 y Fn(?)2437 4424 y Fo(;)17 b Fp(0\))28 b(=)g Fo(E)6 b Fp(.)45 b(F)-8 b(or)32 b(example)386 4540 y(if)j Fo(@)5 b(h=@)g(x)750 4555 y Fj(2)p Fm(n)p Fn(\000)p Fj(1)957 4540 y Fk(6)p Fp(=)32 b(0)j(w)m(e)i(obtain)e Fo(x)1657 4555 y Fj(2)p Fm(n)p Fn(\000)p Fj(1)1862 4540 y Fp(=)e Fo(g)t Fp(\()o Fo(u;)17 b(E)6 b Fp(\))34 b(with)i Fo(u)c Fp(=)h(\()o Fo(x)2823 4555 y Fj(1)2863 4540 y Fo(;)17 b(:)g(:)g(:)f(;)h(x)3137 4555 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)3310 4540 y Fp(\).)386 4656 y(Here)37 b(w)m(e)h(assume)g(\()p Fo(u;)17 b(E)6 b Fp(\))36 b(is)h(in)g(a)f (neigh)m(b)s(orho)s(o)s(d)h(of)f(\(0)p Fo(;)17 b(E)2639 4671 y Fj(0)2678 4656 y Fp(\),)38 b Fo(E)2853 4671 y Fj(0)2927 4656 y Fp(=)c Fo(h)p Fp(\()p Fo(x)3186 4671 y Fj(0)3226 4656 y Fp(\))h(=)386 4773 y Fo(h)p Fp(\(0\).)43 b(W)-8 b(e)33 b(obtain)1592 4890 y Fo(du)p 1592 4935 107 4 v 1593 5026 a(d\034)1736 4958 y Fp(=)28 b Fo(f)11 b Fp(\()o Fo(u;)17 b(E)6 b Fp(\))o Fo(;)947 b Fp(\(1.17\))386 5155 y(where)41 b Fo(f)11 b Fp(\()o Fo(u;)17 b(E)6 b Fp(\))39 b(=)1142 5074 y Fi(\000)1188 5155 y Fp(\()o Fo(v)1272 5170 y Fm(h)1317 5155 y Fp(\))1355 5184 y Fj(1)1395 5155 y Fp(\()p Fo(u;)17 b(g)t Fp(\()n Fo(u;)g(E)6 b Fp(\))o(\))p Fo(;)17 b(:)g(:)g(:)f(;)h Fp(\()p Fo(v)2177 5170 y Fm(h)2222 5155 y Fp(\))2260 5184 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)2432 5155 y Fp(\()p Fo(u;)g(g)t Fp(\()o Fo(u;)g(E)6 b Fp(\))o(\))2911 5074 y Fi(\001)2956 5155 y Fp(.)65 b(The)40 b(or-)386 5274 y(bit)49 b(of)f Fo(v)728 5289 y Fm(h)821 5274 y Fp(along)g Fo(v)53 b Fp(corresp)s(onds)d(to)e Fo(u)54 b Fp(=)h(0)p Fo(;)114 b(E)61 b Fp(=)55 b Fo(E)2650 5289 y Fj(0)2738 5274 y Fp(\(in)49 b(whic)m(h)h(case)386 5390 y Fo(f)11 b Fp(\(0)p Fo(;)17 b(E)648 5405 y Fj(0)687 5390 y Fp(\))50 b(=)g(0)45 b(\).)83 b(If)45 b(det)17 b(\()p Fo(@)5 b(f)1547 5405 y Fm(i)1577 5390 y Fo(=@)g(u)1738 5405 y Fm(j)1774 5390 y Fp(\(0)p Fo(;)17 b(E)1977 5405 y Fj(0)2016 5390 y Fp(\)\))50 b Fk(6)p Fp(=)g(0)45 b(there)i(will)f(b)s (e)g(a)g(smo)s(oth)386 5506 y(family)c(of)g(\014xed)h(p)s(oin)m(ts)f (of)48 b(\(1.17\),)c Fo(u)f Fp(=)g Fo(u)p Fp(\()o Fo(E)6 b Fp(\),)45 b(in)d(a)f(neigh)m(b)s(orho)s(o)s(d)h(of)f Fo(E)3335 5521 y Fj(0)386 5623 y Fp(\(with)47 b Fo(u)p Fp(\()p Fo(E)826 5638 y Fj(0)865 5623 y Fp(\))52 b(=)g(0\).)86 b(This)48 b(situation)f(is)h(en)m(tirely)g(analogous)f(to)f(the)i(case) p eop end %%Page: 8 8 TeXDict begin 8 7 bop 386 259 a Fl(8)793 b(IRA)24 b(HERBST)i(AND)e (ERIK)h(SKIBSTED)386 459 y Fo(v)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))49 b(=)834 384 y Fi(P)956 459 y Fo(x)1011 474 y Fm(i)1040 459 y Fo(@)5 b(=@)g(x)1256 474 y Fm(i)1331 459 y Fp(discussed)48 b(ab)s(o)m(v)m(e)f(and)e(w)m(e)i(can)f(de\014ne)g (stabilit)m(y)h(of)386 575 y(orbits)33 b(in)g Fo(M)43 b Fp(in)33 b(terms)g(of)f(the)h(stabilit)m(y)h(of)e(the)h(\014xed)h(p)s (oin)m(ts)f Fo(u)p Fp(\()p Fo(E)6 b Fp(\).)486 691 y(If)47 b(a)g(pro)s(of)f(of)h(absence)i(of)d(c)m(hannels)j(is)f(con)m (templated)h(along)e(the)g(lines)386 807 y(carried)35 b(out)g(in)g(this)h(pap)s(er,)g(it)f(is)g(necessary)j(that)c(lo)m(w)i (order)f(resonances)i(do)386 924 y(not)k(o)s(ccur)g(at)f(more)h(than)g (a)g(discrete)h(set)g(of)e(energies.)70 b(In)41 b(particular,)i(the)386 1040 y(equations)34 b(\(1.17\))e(should)h(not)f(ha)m(v)m(e)i(a)f (Hamiltonian)f(structure.)486 1156 y(The)38 b(only)h(place)g(where)g (the)f(Hamiltonian)h(nature)f(of)g(the)g(equations)h(ap-)386 1272 y(p)s(eared)24 b(ab)s(o)m(v)m(e)g(w)m(as)h(where)g(w)m(e)f(used)h (conserv)-5 b(ation)25 b(of)e(energy)-8 b(.)41 b(T)-8 b(o)24 b(bring)f(in)h(the)386 1389 y(symplectic)29 b(form)e Fo(!)j Fp(w)m(e)e(in)m(tro)s(duce)g(what)f(turns)g(out)g(to)g(b)s(e)g (a)f(more)h(restrictiv)m(e)386 1505 y(but)33 b(more)g(geometric)g (condition)g(\(see)h(Remark)f(1.5)f(for)g(an)h(in)m(terpretation\):)386 1661 y FC(Lemma)39 b(1.4.)j Fg(Fix)34 b(an)h(op)-5 b(en)34 b(set)h Fo(U)j Fk(\022)28 b Fo(M)10 b Fg(.)534 1798 y Fp(\(a\))41 b Fg(Supp)-5 b(ose)45 b Fk(L)1151 1813 y Fm(v)1192 1798 y Fo(!)50 b Fp(=)d Fo(\013)q(!)h Fg(in)d Fo(U)56 b Fg(for)45 b(some)f Fo(\013)k Fk(2)f Fo(C)2575 1761 y Fn(1)2650 1798 y Fp(\()p Fo(U)10 b Fp(\))p Fg(.)77 b(Supp)-5 b(ose)44 b(in)700 1914 y(addition)35 b(that)g Fo(v)t(h)27 b Fp(=)h(0)35 b Fg(in)f Fo(U)10 b Fg(.)45 b(Then)35 b Fp([)p Fo(v)t(;)17 b(v)2297 1929 y Fm(h)2341 1914 y Fp(])28 b(=)f Fk(\000)p Fo(\013)q(v)2686 1929 y Fm(h)2766 1914 y Fg(in)35 b Fo(U)10 b Fg(.)529 2030 y Fp(\(b\))41 b Fg(Supp)-5 b(ose)32 b Fo(v)k Fg(is)31 b(nonzer)-5 b(o)31 b(in)h Fo(U)43 b Fg(and)31 b(for)h(any)g(smo)-5 b(oth)31 b(function)h Fo(h)g Fg(on)g Fo(U)700 2146 y Fg(satisfying)k Fo(v)t(h)30 b Fp(=)f(0)36 b Fg(in)g(a)g(neighb)-5 b(orho)g(o)g(d)34 b(of)i(a)f(p)-5 b(oint)36 b(of)g Fo(U)10 b Fg(,)37 b Fo(v)i Fg(satis\014es)700 2262 y Fp([)q Fo(v)t(;)17 b(v)870 2277 y Fm(h)914 2262 y Fp(])28 b(=)f Fk(\000)p Fo(\013)q(v)1259 2277 y Fm(h)1339 2262 y Fg(in)35 b(this)g(neighb)-5 b(orho)g(o)g(d.)43 b(Then)34 b Fk(L)2588 2277 y Fm(v)2628 2262 y Fo(!)d Fp(=)d Fo(\013)q(!)38 b Fg(in)c Fo(U)10 b Fg(.)386 2419 y(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)36 b(shall)f(use)h(the)g(general)f(relations)h Fo(dh)p Fp(\()p Fo(w)s Fp(\))31 b(=)h Fo(!)t Fp(\()p Fo(v)2709 2434 y Fm(h)2753 2419 y Fo(;)17 b(w)s Fp(\),)35 b([)p Fk(L)3066 2434 y Fm(v)3106 2419 y Fo(;)17 b(i)3183 2434 y Fm(w)3240 2419 y Fp(])32 b(=)386 2535 y Fo(i)419 2550 y Fj([)p Fm(v)r(;w)r Fj(])607 2535 y Fp(and)j([)p Fk(L)895 2550 y Fm(w)952 2535 y Fo(;)17 b(d)p Fp(])32 b(=)g(0.)52 b(Here)37 b Fo(i)1609 2550 y Fm(w)1701 2535 y Fp(represen)m(ts)h(in)m(terior)e (pro)s(duct)g(with)g Fo(w)i Fp(\(see)386 2651 y(for)32 b(example)i([C)q(,)e(p.)44 b(84])32 b(or)g([A2,)h(p.)43 b(198]\).)486 2767 y(F)-8 b(or)31 b(\(a\))h(w)m(e)i(compute)g(in)f Fo(U)569 2924 y(i)602 2940 y Fj([)p Fm(v)r(;v)712 2952 y Ff(h)753 2940 y Fj(])777 2924 y Fo(!)e Fp(=)d([)p Fk(L)1069 2939 y Fm(v)1109 2924 y Fo(;)17 b(i)1186 2939 y Fm(v)1220 2951 y Ff(h)1265 2924 y Fp(])p Fo(!)31 b Fp(=)d Fk(L)1557 2939 y Fm(v)1597 2924 y Fo(dh)22 b Fk(\000)h Fo(i)1859 2939 y Fm(v)1893 2951 y Ff(h)1938 2924 y Fo(\013)q(!)31 b Fp(=)c Fo(d)p Fk(L)2316 2939 y Fm(v)2357 2924 y Fo(h)22 b Fk(\000)h Fo(i)2568 2939 y Fm(\013v)2647 2951 y Ff(h)2692 2924 y Fo(!)31 b Fp(=)c Fo(i)2920 2939 y Fn(\000)p Fm(\013v)3054 2951 y Ff(h)3100 2924 y Fo(!)t(:)386 3081 y Fp(Since)34 b Fo(!)h Fp(is)f(non-degenerate)f(w)m(e)h(conclude)g(\(a\).)486 3197 y(As)f(for)f(\(b\))g(w)m(e)i(use)f(the)g(same)h(computation)f(to)f (conclude)i(that)1447 3354 y Fo(i)1480 3369 y Fm(v)1514 3381 y Ff(h)1559 3354 y Fp(\()p Fk(\000L)1743 3369 y Fm(v)1784 3354 y Fo(!)26 b Fp(+)c Fo(\013)q(!)t Fp(\))k(=)i(0)386 3511 y(in)k(op)s(en)h(subsets)h(where)f Fo(v)t(h)28 b Fp(=)f(0.)43 b(Since)34 b Fo(v)i Fp(is)c(nonzero)h(there)g(are)f (su\016cien)m(tly)386 3627 y(man)m(y)h(c)m(hoices)i(of)d Fo(h)h Fp(to)f(conclude)i(from)e(this)h(that)g(indeed)h Fk(L)2710 3642 y Fm(v)2750 3627 y Fo(!)d Fp(=)d Fo(\013)q(!)t Fp(.)196 b Fe(\003)386 3784 y Fg(R)-5 b(emark)37 b Fp(1.5)p Fg(.)d Fp(By)24 b(in)m(tegrating)g(the)g(condition)h(of)e(Lemma)h(1.4)f (\(a\),)i Fk(L)2984 3799 y Fm(v)3025 3784 y Fo(!)31 b Fp(=)d Fo(\013)q(!)t Fp(,)386 3900 y(w)m(e)34 b(obtain)1239 4058 y(\()p Fo(\036)1335 4017 y Fm(v)1335 4083 y(t)1375 4058 y Fp(\))1413 4017 y Fn(\003)1453 4058 y Fo(!)d Fp(=)c(exp)1814 3948 y Fi(\020)1873 3923 y(Z)1973 3949 y Fm(t)1929 4148 y Fj(0)2019 4058 y Fo(\013)c Fk(\016)f Fo(\036)2234 4017 y Fm(v)2234 4083 y(s)2274 4058 y Fo(ds)2371 3948 y Fi(\021)2431 4058 y Fo(!)t(:)386 4246 y Fp(In)j(particular)g(if)g Fk(L)1093 4261 y Fm(v)1134 4246 y Fo(!)31 b Fp(=)c Fo(\013)q(!)h Fp(holds)e(in)f Fo(M)36 b Fp(and)25 b Fo(\036)2205 4210 y Fm(v)2205 4271 y(t)2270 4246 y Fp(is)h(a)f(global)f(\015o)m(w)i(w)m (e)g(see)g(that)386 4362 y(the)33 b(di\013eomorphisms)i Fo(\036)1337 4326 y Fm(v)1337 4387 y(t)1410 4362 y Fp(preserv)m(e)g (the)e(family)g(of)f(Lagrangian)f(manifolds.)486 4479 y(Con)m(v)m(ersely)k(one)d(ma)m(y)h(readily)g(pro)m(v)m(e)g(that)f(if)g Fo(\036)2310 4442 y Fm(v)2310 4503 y(t)2382 4479 y Fp(is)h(a)f(global)f (\015o)m(w)i(and)f(the)386 4595 y(di\013eomorphisms)j Fo(\036)1169 4559 y Fm(v)1169 4619 y(t)1243 4595 y Fp(preserv)m(e)h (the)e(family)f(of)g(Lagrangian)g(manifolds,)h(then)386 4711 y(indeed)g Fk(L)764 4726 y Fm(v)804 4711 y Fo(!)d Fp(=)d Fo(\013)q(!)35 b Fp(for)e(some)g(smo)s(oth)g Fo(\013)q Fp(.)386 4867 y Fg(Example)j Fp(1.6)p Fg(.)h Fp(W)-8 b(e)27 b(giv)m(e)g(another)g(simple)i(example)f(from)e(Riemannian)i (geom-)386 4983 y(etry)-8 b(.)44 b(Consider)34 b(the)f(sym)m(b)s(ol)h Fo(h)e Fp(on)h(\()p FC(R)1874 4947 y Fj(2)1935 4983 y Fk(n)22 b(f)p Fp(0)p Fk(g)o Fp(\))g Fk(\002)h FC(R)2399 4947 y Fj(2)1066 5189 y Fo(h)28 b Fp(=)f Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1673 5121 y(1)p 1673 5166 49 4 v 1673 5257 a(2)1732 5108 y Fi(\000)1777 5189 y Fo(x)1832 5148 y Fj(2)1832 5214 y(1)1894 5189 y Fp(+)22 b Fo(ax)2098 5148 y Fj(2)2098 5214 y(2)2138 5108 y Fi(\001)2184 5130 y Fn(\000)p Fj(1)2278 5189 y Fo(\030)2326 5148 y Fj(2)2365 5189 y Fp(;)45 b Fo(a)27 b(>)h Fp(0)p Fo(:)430 b Fp(\(1.18\))386 5381 y(Let)37 b Fo(v)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))35 b(=)986 5306 y Fi(P)1091 5381 y Fp(\()p Fo(x)1184 5396 y Fm(i)1212 5381 y Fo(@)5 b(=@)g(x)1428 5396 y Fm(i)1484 5381 y Fp(+)25 b Fo(\030)1628 5396 y Fm(i)1656 5381 y Fo(@)5 b(=@)g(\030)1860 5396 y Fm(i)1889 5381 y Fp(\).)58 b(Then)38 b(the)g(v)m(ector)g(\014eld)g Fo(v)j Fp(and)c(the)386 5497 y(Hamitonian)d(v)m(ector)i(\014eld)e Fo(v)1475 5512 y Fm(h)1555 5497 y Fp(ful\014ll)g(the)h(condition)f (\(1\){\(3\))g(along)f(the)i(p)s(osi-)386 5623 y(tiv)m(e)27 b(orbit)g(of)f Fo(v)k Fp(originating)c(at)g(\(1)10 b(+)g(2)p Fo(E)c Fp(\))1932 5587 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2095 5623 y Fp(\(1)p Fo(;)17 b Fp(0;)2319 5538 y Fk(p)p 2401 5538 127 4 v 2401 5623 a Fp(2)p Fo(E)6 b(;)17 b Fp(0\),)27 b Fo(E)34 b(>)27 b Fp(0.)41 b(Here)28 b(w)m(e)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)809 b(9)386 459 y Fp(ha)m(v)m(e)32 b(tak)m(en)g(the)g Fo(S)37 b Fp(in)31 b(condition)h(\(1\))e(to)h(b)s(e)g(a)g(subset)i(of)d (the)i(unit-sphere)g Fo(S)3308 423 y Fj(3)3348 459 y Fp(.)386 575 y(Notice)26 b(also)g(that)f(\()p Fo(\036)1174 539 y Fm(v)1174 600 y(t)1215 575 y Fp(\))1253 539 y Fn(\003)1292 575 y Fo(!)31 b Fp(=)d(exp)q(\(2)p Fo(t)p Fp(\))p Fo(!)t Fp(,)e(and)g(therefore)g Fk(L)2569 590 y Fm(v)2609 575 y Fo(!)31 b Fp(=)d(2)p Fo(!)t Fp(.)40 b(After)26 b(lin-)386 700 y(earizing)i(the)f(reduced)i(\015o)m(w)g(\(1.17\))e(w)m(e)h(\014nd) g(the)g(eigen)m(v)-5 b(alues)29 b Fk(\000)2807 616 y(p)p 2891 616 127 4 v 2891 700 a Fp(2)p Fo(E)5 b Fp(\()3055 629 y Fk(p)p 3138 629 52 4 v 71 x Fo(a)12 b Fp(+)f(1\))386 826 y(and)587 742 y Fk(p)p 670 742 127 4 v 84 x Fp(2)p Fo(E)6 b Fp(\()835 754 y Fk(p)p 918 754 52 4 v 72 x Fo(a)30 b Fk(\000)g Fp(1\),)46 b(and)e(w)m(e)h(conclude)g(that)e(the)i(family)f (of)f(\014xed)i(p)s(oin)m(ts)386 942 y(consists)c(of)e(sinks)i(for)e Fo(a)h Fk(2)f Fp(\(0)p Fo(;)17 b Fp(1\))39 b(and)g(saddle)i(p)s(oin)m (ts)f(for)f Fo(a)g(>)g Fp(1.)64 b(If)3136 870 y Fk(p)p 3219 870 V 72 x Fo(a)39 b Fp(is)386 1058 y(irrational)g(there)h(are)g (no)f(resonances)i(\(of)e(an)m(y)h(order\).)64 b(The)41 b(sym)m(b)s(ol)f(\(1.18\))386 1175 y(needs)34 b(to)e(b)s(e)h (regularized)h(at)e Fo(x)c Fp(=)f(0)33 b(\(for)f(the)h(quan)m (tization\).)486 1359 y(This)i(pap)s(er)g(is)g(organized)g(as)g(follo)m (ws:)48 b(In)35 b(Section)g(2)f(w)m(e)i(elab)s(orate)e(on)h(all)386 1475 y(tec)m(hnical)h(conditions)f(needed)h(for)e(Theorem)i(1.1)e(and)h (giv)m(e)g(a)f(more)h(detailed)386 1591 y(outline)g(of)e(its)i(pro)s (of,)f(cf.)48 b(the)35 b(steps)g(I\){I)s(I)s(I\))f(indicated)h(ab)s(o)m (v)m(e.)49 b(In)35 b(Section)g(3)386 1707 y(w)m(e)g(ha)m(v)m(e)g (collected)g(a)f(few)g(tec)m(hnical)h(preliminaries.)49 b(In)34 b(Section)h(4)f(w)m(e)g(pro)m(v)m(e)386 1824 y(the)f Fo(t)589 1787 y Fn(\000)p Fm(\016)715 1824 y Fp({lo)s(calization,)g(cf.)45 b(step)33 b(I\),)g(while)h(the)g(lo)s (calization)f(of)f(\000)h(is)g(giv)m(en)h(in)386 1940 y(Section)j(5.)53 b(Finally)-8 b(,)38 b(Section)e(6)g(is)h(dev)m(oted)g (to)f(the)g(Mourre)h(theory)g(for)e(this)386 2056 y(observ)-5 b(able.)68 b(W)-8 b(e)40 b(complete)i(the)e(pro)s(of)g(of)g(Theorem)h (1.1)f(in)g(Section)i(7)e(and)386 2172 y(giv)m(e)33 b(a)g(few)g (missing)h(details)f(of)f(the)h(pro)s(of)f(of)g(Theorem)i(1.2)e(in)h (Section)g(8.)711 2418 y(2.)48 b Fq(Technical)38 b(conditions)g(and)g (outline)g(of)h(pr)n(oof)486 2592 y Fp(W)-8 b(e)40 b(\014x)h(\()p Fo(!)906 2607 y Fj(0)945 2592 y Fo(;)17 b(\030)1032 2607 y Fj(0)1071 2592 y Fp(\))40 b Fk(2)h Fo(S)1322 2556 y Fm(n)p Fn(\000)p Fj(1)1486 2592 y Fk(\002)28 b FC(R)1675 2556 y Fm(n)1762 2592 y Fp(and)40 b(a)g(small)g(op)s(en)h(neigh)m(b)s (orho)s(o)s(d)f Fo(I)3217 2607 y Fj(0)3296 2592 y Fp(of)386 2709 y Fo(E)458 2724 y Fj(0)535 2709 y Fp(=)d Fo(h)p Fp(\()p Fo(r)s(!)850 2724 y Fj(0)889 2709 y Fo(;)17 b(\030)976 2724 y Fj(0)1015 2709 y Fp(\))38 b(as)h(in)f(Section)h(1.)61 b(W)-8 b(e)38 b(shall)h(elab)s(orate)f(on)g(conditions)i(on)386 2825 y(the)c(real-v)-5 b(alued)35 b(sym)m(b)s(ol)i Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o(,)36 b(see)h(\(H1\){\(H8\))d(b)s (elo)m(w.)53 b(F)-8 b(or)34 b(con)m(v)m(enience)386 2941 y(w)m(e)26 b(remo)m(v)m(e)h(a)e(p)s(ossible)i(singularit)m(y)f(at)f Fo(x)j Fp(=)g(0)d(caused)h(b)m(y)g(the)g(imp)s(osed)g(\(lo)s(cal\))386 3057 y(homogeneit)m(y)42 b(assumption)g(of)e(Section)i(1.)68 b(This)41 b(ma)m(y)h(b)s(e)f(done)g(as)g(follo)m(ws.)386 3174 y(Let)c Fk(N)647 3189 y Fj(0)724 3174 y Fp(b)s(e)g(as)g(small)h (op)s(en)g(neigh)m(b)s(orho)s(o)s(d)f(of)f(\()p Fo(!)2317 3189 y Fj(0)2356 3174 y Fo(;)17 b(\030)2443 3189 y Fj(0)2482 3174 y Fp(\).)57 b(W)-8 b(e)38 b(shall)g(no)m(w)g(and)386 3290 y(henceforth)c(assume)g(that)e(for)g(some)h Fo(r)1851 3305 y Fj(0)1919 3290 y Fo(>)27 b Fp(0)564 3445 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(h)p Fp(\()q Fo(r)1112 3460 y Fj(0)1157 3445 y Fp(^)-55 b Fo(x;)17 b(\030)5 b Fp(\))27 b Fo(in)h Fk(C)1534 3460 y Fj(0)1602 3445 y Fp(:=)g Fk(f)o Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b Fk(j)h Fp(\()6 b(^)-55 b Fo(x;)17 b(\030)5 b Fp(\))27 b Fk(2)h(N)2514 3460 y Fj(0)2553 3445 y Fo(;)17 b Fk(j)p Fo(x)p Fk(j)27 b Fo(>)h(r)2883 3460 y Fj(0)2922 3445 y Fk(g)p Fo(;)564 3596 y(h)g Fk(2)g Fo(C)819 3555 y Fn(1)893 3596 y Fp(\()p FC(R)1015 3555 y Fm(n)1084 3596 y Fk(\002)23 b FC(R)1268 3555 y Fm(n)1314 3596 y Fp(\))p Fo(:)3177 3527 y Fp(\(H1\))386 3770 y(Notice)42 b(that)g(this)g(mo)s (di\014cation)h(in)m(tuitiv)m(ely)h(is)e(irrelev)-5 b(an)m(t)43 b(for)e(the)i(issue)g(of)386 3887 y(Theorem)k(1.1)f(\(whic)m(h)h (concerns)h(states)e(propagating)g(linearly)h(in)f(time)g(in)386 4003 y(con\014guration)33 b(space\).)486 4119 y(W)-8 b(e)33 b(assume)h(that)e(for)g(some)h Fo(r)m(;)17 b(l)30 b Fk(\025)e Fp(0)452 4319 y Fo(h)g Fk(2)g Fo(S)696 4208 y Fi(\020)755 4319 y Fk(h)p Fo(\030)5 b Fk(i)880 4270 y Fm(r)918 4319 y Fk(h)p Fo(x)p Fk(i)1051 4270 y Fm(l)1077 4319 y Fo(;)17 b(g)1168 4334 y Fj(0)1207 4208 y Fi(\021)1266 4319 y Fp(;)66 b Fo(g)1406 4334 y Fj(0)1473 4319 y Fp(=)27 b Fk(h)p Fo(x)p Fk(i)1709 4270 y Fn(\000)p Fj(2)1803 4319 y Fo(dx)1909 4278 y Fj(2)1971 4319 y Fp(+)22 b Fo(d\030)2168 4278 y Fj(2)2207 4319 y Fo(;)65 b Fk(h)p Fo(x)p Fk(i)28 b Fp(=)2563 4238 y Fi(\000)2609 4319 y Fp(1)22 b(+)g Fk(j)p Fo(x)p Fk(j)2889 4278 y Fj(2)2928 4238 y Fi(\001)2974 4260 y Fj(1)p Fm(=)p Fj(2)3084 4319 y Fo(;)66 b Fp(\(H2\))386 4519 y(and)33 b(that)639 4692 y Fo(H)i Fp(=)27 b Fo(h)914 4651 y Fm(w)971 4692 y Fp(\()p Fo(x;)17 b(p)p Fp(\))28 b Fo(is)g(essential)r(l)r(y)k(sel)r(f)p Fk(\000)-11 b Fo(ad)g(j)6 b(oint)29 b(on)f(C)2616 4651 y Fn(1)2609 4717 y Fj(0)2691 4692 y Fp(\()p FC(R)2813 4651 y Fm(n)2859 4692 y Fp(\))p Fo(:)253 b Fp(\(H3\))386 4866 y(\(See)33 b(Section)h(3)e(for)g(notation.\))386 5050 y Fg(R)-5 b(emark.)33 b Fp(There)23 b(is)f(some)h(freedom)f(in)h(c)m(ho)s(osing)f (a)g(global)f(condition)i(lik)m(e)g(\(H2\),)386 5178 y(for)37 b(example)i(it)e(su\016ces)j(to)d(ha)m(v)m(e)h(\(H2\))f(with)h Fo(g)2228 5193 y Fj(0)2305 5178 y Fp(replaced)g(b)m(y)h Fk(h)p Fo(x)p Fk(i)2968 5129 y Fn(\000)p Fj(2)p Fm(\016)3089 5138 y Fh(1)3128 5178 y Fo(dx)3234 5142 y Fj(2)3299 5178 y Fp(+)386 5306 y Fk(h)p Fo(x)p Fk(i)519 5257 y Fj(2)p Fm(\016)585 5266 y Fh(2)624 5306 y Fo(d\030)723 5269 y Fj(2)794 5306 y Fp(with)33 b(0)28 b Fk(\024)g Fo(\016)1241 5321 y Fj(2)1308 5306 y Fo(<)g(\016)1455 5321 y Fj(1)1522 5306 y Fk(\024)g Fp(1)33 b(.)486 5490 y(W)-8 b(e)33 b(assume)1396 5623 y(\(1.2\))o({)s(\(1.4\))27 b Fo(f)11 b(or)30 b(E)j Fk(2)c Fo(I)2299 5638 y Fj(0)2338 5623 y Fo(:)812 b Fp(\(H4\))p eop end %%Page: 10 10 TeXDict begin 10 9 bop 386 259 a Fl(10)755 b(IRA)24 b(HERBST)i(AND)e (ERIK)h(SKIBSTED)486 459 y Fp(W)-8 b(e)48 b(de\014ne)i Fo(!)1028 474 y Fm(n)1075 459 y Fp(\()p Fo(E)6 b Fp(\))54 b(=)g Fo(!)t Fp(\()p Fo(E)6 b Fp(\),)52 b(and)c(shrinking)i Fo(I)2401 474 y Fj(0)2489 459 y Fp(if)e(necessary)j(w)m(e)e(pic)m(k)386 575 y(smo)s(oth)33 b(functions)1306 751 y Fo(!)1367 766 y Fj(1)1406 751 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(:)g(:)g(:)f(;)h(!) 1840 766 y Fm(n)p Fn(\000)p Fj(1)1976 751 y Fp(\()p Fo(E)6 b Fp(\))28 b Fk(2)g Fo(S)2318 710 y Fm(n)p Fn(\000)p Fj(1)386 928 y Fp(suc)m(h)45 b(that)e Fo(!)900 943 y Fj(1)940 928 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(:)g(:)g(:)e(;)i(!) 1373 943 y Fm(n)1420 928 y Fp(\()p Fo(E)6 b Fp(\))43 b(are)h(m)m(utually)h(orthogonal.)76 b(W)-8 b(e)44 b(de\014ne,)j(cf.) 386 1044 y(\(1.5\))o(,)g Fo(x)715 1059 y Fm(j)799 1044 y Fp(=)f Fo(x)31 b Fk(\001)e Fo(!)1125 1059 y Fm(j)1161 1044 y Fp(\()p Fo(E)6 b Fp(\))44 b(for)f Fo(j)53 b Fk(\024)47 b Fo(n)p Fp(,)g Fo(u)1924 1059 y Fm(j)2007 1044 y Fp(=)f Fo(x)2184 1059 y Fm(j)2221 1044 y Fo(=x)2325 1059 y Fm(n)2416 1044 y Fp(and)e Fo(\021)2665 1059 y Fm(j)2748 1044 y Fp(=)j(\()p Fo(\030)26 b Fk(\000)d Fo(\030)5 b Fp(\()o Fo(E)h Fp(\)\))30 b Fk(\001)386 1160 y Fo(!)447 1175 y Fm(j)483 1160 y Fp(\()p Fo(E)6 b Fp(\))40 b(for)g Fo(j)47 b Fk(\024)42 b Fo(n)27 b Fk(\000)h Fp(1)41 b(and)f Fo(\026)h Fp(=)g(\()p Fo(\030)26 b Fk(\000)d Fo(\030)5 b Fp(\()o Fo(E)h Fp(\)\))27 b Fk(\001)h Fo(!)2324 1175 y Fm(n)2370 1160 y Fp(\()p Fo(E)6 b Fp(\).)67 b(Let)41 b Fo(w)i Fp(=)e(\()p Fo(u;)17 b(\021)t Fp(\))40 b(=)386 1276 y(\()p Fo(u)480 1291 y Fj(1)519 1276 y Fo(;)17 b(:)g(:)g(:)f(;)h(u)794 1291 y Fm(n)p Fn(\000)p Fj(1)930 1276 y Fo(;)g(\021)1022 1291 y Fj(1)1061 1276 y Fo(;)g(:)g(:)g(:)f(;)h(\021)1328 1291 y Fm(n)p Fn(\000)p Fj(1)1465 1276 y Fp(\).)486 1392 y(As)41 b(for)g(the)h(matrix)g Fo(B)5 b Fp(\()p Fo(E)h Fp(\))41 b(of)48 b(\(1.7\))41 b(in)h(these)g(co)s(ordinates)g(w)m(e)h (need)f(the)386 1509 y(condition:)741 1685 y Fo(T)14 b(he)28 b(r)s(eal)i(par)s(t)d(of)39 b(al)r(l)30 b(eig)t(env)t(al)r(ues) e(of)38 b(B)5 b Fp(\()p Fo(E)h Fp(\))28 b Fo(is)g(nonz)t(er)s(o)741 1836 y(f)11 b(or)30 b(E)k Fk(2)28 b Fo(I)1164 1851 y Fj(0)1203 1836 y Fo(:)1947 b Fp(\(H5\))486 2018 y(Let)26 b(us)i(order)e(the)i(eigen)m(v)-5 b(alues)28 b(as)f Fo(\014)1858 1982 y Fm(s)1852 2043 y Fj(1)1894 2018 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(:)g(:)g(:)f(;)h(\014)2328 1982 y Fm(s)2322 2043 y(n)2365 2024 y Ff(s)2402 2018 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(\014)2661 1982 y Fm(u)2655 2043 y Fj(1)2705 2018 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(:)g(:)g(:)f(;)h(\014)3139 1982 y Fm(u)3133 2043 y(n)3176 2024 y Ff(u)3221 2018 y Fp(\()p Fo(E)6 b Fp(\))386 2136 y(where)31 b(Re)797 2055 y Fi(\000)842 2136 y Fo(\014)903 2100 y Fm(s)897 2161 y(j)940 2136 y Fp(\()p Fo(E)6 b Fp(\))1094 2055 y Fi(\001)1167 2136 y Fo(<)28 b Fp(0)h(\()p Fo(\014)1448 2100 y Fm(s)1442 2161 y(j)1484 2136 y Fp(\()p Fo(E)6 b Fp(\))30 b(are)g(the)g(stable)h(ones\))f(and)g(Re)2844 2055 y Fi(\000)2890 2136 y Fo(\014)2951 2100 y Fm(u)2945 2161 y(j)2995 2136 y Fp(\()p Fo(E)6 b Fp(\))3149 2055 y Fi(\001)3222 2136 y Fo(>)28 b Fp(0)386 2261 y(\()i Fo(\014)515 2225 y Fm(u)509 2286 y(j)560 2261 y Fp(\()p Fo(E)6 b Fp(\))30 b(are)g(the)h(unstable)g(ones\).)44 b(Let)30 b Fo(\014)6 b Fp(\()p Fo(E)g Fp(\))30 b(refer)h(to)f(the)g FC(C)2754 2225 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)2957 2261 y Fp({v)m(ector)h(of)386 2381 y(eigen)m(v)-5 b(alues)34 b(\()p Fo(\014)989 2345 y Fm(s)983 2406 y Fj(1)1026 2381 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(:)g(:)g(:)f(;)h(\014)1460 2345 y Fm(u)1454 2406 y(n)1497 2387 y Ff(u)1541 2381 y Fp(\()p Fo(E)6 b Fp(\)\))33 b(coun)m(ted)g(with)h(m)m(ultiplicit)m(y) -8 b(.)486 2498 y(W)g(e)33 b(are)f(in)m(terested)j(in)e(the)g(case)1530 2674 y Fo(n)1588 2633 y Fm(u)1661 2674 y Fp(=)28 b Fo(n)1823 2633 y Fm(u)1868 2674 y Fp(\()p Fo(E)6 b Fp(\))27 b Fk(\025)i Fp(1)p Fo(:)946 b Fp(\(H6\))486 2850 y(Let)46 b Fo(V)753 2814 y Fm(s)790 2850 y Fp(\()o Fo(E)6 b Fp(\))47 b(and)g Fo(V)1272 2814 y Fm(u)1317 2850 y Fp(\()p Fo(E)6 b Fp(\))46 b(b)s(e)h(the)g(sum)g(of)f(the)h(generalized)h(eigenspaces)386 2967 y(of)31 b Fo(B)5 b Fp(\()p Fo(E)h Fp(\))32 b(correp)s(onding)g(to) f(stable)h(and)g(unstable)h(eigen)m(v)-5 b(alues,)34 b(resp)s(ectiv)m(ely)-8 b(.)386 3083 y(Then)34 b(w)m(e)f(ha)m(v)m(e)h (the)f(decomp)s(osition)1340 3259 y FC(C)1421 3218 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)1621 3259 y Fp(=)28 b Fo(V)1803 3218 y Fm(s)1840 3259 y Fp(\()p Fo(E)6 b Fp(\))22 b Fk(\010)h Fo(V)2194 3218 y Fm(u)2239 3259 y Fp(\()p Fo(E)6 b Fp(\))p Fo(:)486 3435 y Fp(Using)39 b(basis)h(v)m(ectors)g(resp)s(ecting)g (this)f(structure)h(w)m(e)g(can)f(\014nd)g(a)g(smo)s(oth)386 3552 y Fo(M)480 3567 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)653 3552 y Fp(\()p FC(C)p Fp(\))32 b({v)-5 b(alued)33 b(function)g Fo(T)14 b Fp(\()p Fo(E)6 b Fp(\))32 b(suc)m(h)i(that)981 3736 y Fo(T)14 b Fp(\()o Fo(E)6 b Fp(\))1205 3688 y Fn(\000)p Fj(1)1300 3736 y Fo(B)f Fp(\()p Fo(E)h Fp(\))p Fo(T)14 b Fp(\()o Fo(E)6 b Fp(\))28 b(=)g(diag)17 b(\()p Fo(B)2202 3695 y Fm(s)2239 3736 y Fp(\()p Fo(E)6 b Fp(\))p Fo(;)17 b(B)2516 3695 y Fm(u)2561 3736 y Fp(\()p Fo(E)6 b Fp(\)\))p Fo(:)394 b Fp(\(2.1\))486 3912 y(W)-8 b(e)42 b(ma)m(y)i(assume)f(the)g (follo)m(wing)g(at)f Fo(E)50 b Fp(=)45 b Fo(E)2275 3927 y Fj(0)2357 3912 y Fp(:)63 b(Corresp)s(onding)43 b(to)f(the)386 4029 y(decomp)s(osition)34 b(in)m(to)e(generalized)i(eigenspaces)748 4205 y FC(C)829 4164 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)1029 4205 y Fp(=)27 b Fo(V)1211 4164 y Fm(s)1270 4205 y Fk(\010)22 b Fo(V)1448 4164 y Fm(u)1520 4205 y Fp(=)28 b Fo(V)1703 4164 y Fm(s)1681 4230 y Fj(1)1761 4205 y Fk(\010)23 b(\001)17 b(\001)g(\001)j(\010)j Fo(V)2178 4164 y Fm(s)2156 4230 y(n)2199 4211 y Ff(s)2258 4205 y Fk(\010)g Fo(V)2437 4164 y Fm(u)2415 4230 y Fj(1)2504 4205 y Fk(\010)f(\001)17 b(\001)g(\001)k(\010)h Fo(V)2920 4164 y Fm(u)2898 4230 y(n)2941 4211 y Ff(u)2986 4205 y Fo(;)748 4372 y(T)14 b Fp(\()o Fo(E)928 4387 y Fj(0)968 4372 y Fp(\))1006 4324 y Fn(\000)p Fj(1)1100 4372 y Fo(B)5 b Fp(\()p Fo(E)1289 4387 y Fj(0)1329 4372 y Fp(\))p Fo(T)14 b Fp(\()o Fo(E)1547 4387 y Fj(0)1587 4372 y Fp(\))28 b(=)f(diag)18 b(\()p Fo(B)2070 4331 y Fm(s)2065 4397 y Fj(1)2107 4372 y Fo(;)f(:)g(:)g(:)f (;)h(B)2405 4331 y Fm(u)2400 4397 y(n)2443 4378 y Ff(u)2487 4372 y Fp(\))p Fo(;)386 4573 y Fp(where)49 b(for)e(all)g(en)m(tries)i Fo(N)1412 4526 y Fj(#)1402 4599 y Fm(j)1529 4573 y Fp(:=)k Fo(B)1764 4526 y Fj(#)1759 4599 y Fm(j)1859 4573 y Fk(\000)33 b Fo(\014)2030 4526 y Fj(#)2024 4599 y Fm(j)2093 4573 y Fp(\()p Fo(E)2203 4588 y Fj(0)2242 4573 y Fp(\))p Fo(I)2323 4606 y Fj(dim)2452 4614 y Fp(\()2490 4606 y Fm(V)2547 4574 y Fh(#)2531 4628 y Ff(j)2601 4614 y Fp(\))2691 4573 y(is)48 b(strictly)h(lo)m(w)m(er)386 4722 y(triangular.)69 b(Giv)m(en)43 b(an)m(y)f Fo(\017)h(>)f Fp(0)f(w)m(e)h(ma)m(y)h(assume)f (\(b)m(y)h(rescaling)f(the)g(basis)386 4839 y(v)m(ectors\))34 b(that)1655 4984 y Fk(k)p Fo(N)1793 4937 y Fj(#)1783 5010 y Fm(j)1856 4984 y Fk(k)28 b(\024)g Fo(\017:)1069 b Fp(\(2.2\))486 5146 y(W)-8 b(e)27 b(in)m(tro)s(duce)g(a)g(v)m(ector)g (of)f(new)i(v)-5 b(ariables)27 b Fo(\015)33 b Fp(=)28 b(\()p Fo(\015)2417 5110 y Fm(s)2453 5146 y Fo(;)17 b(\015)2553 5110 y Fm(u)2598 5146 y Fp(\))28 b(=)f(\()p Fo(\015)2856 5161 y Fj(1)2895 5146 y Fo(;)17 b(:)g(:)g(:)f(;)h(\015)3165 5161 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)3337 5146 y Fp(\))1195 5330 y Fo(\015)33 b Fp(=)27 b Fo(\015)5 b Fp(\()p Fo(w)s Fp(\()o Fo(E)h Fp(\))p Fo(;)17 b(E)6 b Fp(\))28 b(=)f Fo(T)14 b Fp(\()p Fo(E)6 b Fp(\))2218 5282 y Fn(\000)p Fj(1)2312 5330 y Fo(w)s Fp(\()p Fo(E)g Fp(\))p Fo(;)608 b Fp(\(2.3\))386 5506 y(where)36 b Fo(\015)726 5470 y Fm(s)797 5506 y Fp(and)e Fo(\015)1044 5470 y Fm(u)1124 5506 y Fp(are)g(the)h(v)m(ectors)h(of)e(co)s(ordinates)h(of)f(the)h (part)f(of)g Fo(w)s Fp(\()o Fo(E)6 b Fp(\))34 b(in)386 5623 y Fo(V)464 5587 y Fm(s)501 5623 y Fp(\()p Fo(E)6 b Fp(\))33 b(and)f Fo(V)956 5587 y Fm(u)1001 5623 y Fp(\()p Fo(E)6 b Fp(\),)32 b(resp)s(ectiv)m(ely)-8 b(.)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(11)486 459 y Fp(W)-8 b(e)33 b(shall)g(mak)m(e)g(the)g (assumption)h(\(using)g(\\)p Fo(tr)s Fp(")d(to)i(denote)g(transp)s (osed\):)600 624 y Fg(Ther)-5 b(e)50 b(exists)g(a)g(smo)-5 b(oth)49 b(eigenve)-5 b(ctor)49 b Fo(v)t Fp(\()p Fo(E)6 b Fp(\))50 b Fg(of)g Fo(B)5 b Fp(\()p Fo(E)h Fp(\))2764 576 y Fm(tr)2878 624 y Fg(in)600 740 y Fo(E)34 b Fk(2)28 b Fo(I)843 755 y Fj(0)883 740 y Fg(,)k(such)h(that)f Fp(Re)17 b(\()p Fo(\025)p Fp(\()p Fo(E)6 b Fp(\)\))27 b Fo(<)h Fk(\000)p Fp(1)33 b Fg(for)f(the)g(c)-5 b(orr)g(esp)g(onding) 600 857 y(eigenvalue)34 b Fo(\025)p Fp(\()p Fo(E)6 b Fp(\))p Fg(.)3177 733 y Fp(\(H7\))386 1002 y(See)33 b(Remark)g(2.3)g(b) s(elo)m(w)g(for)f(an)h(alternativ)m(e)g(condition.)486 1118 y(The)g(ordering)g(of)f(the)h(eigen)m(v)-5 b(alues)34 b(ma)m(y)g(b)s(e)f(c)m(hosen)h(suc)m(h)g(that)1570 1277 y Fo(\014)1631 1236 y Fm(s)1625 1302 y Fj(1)1667 1277 y Fp(\()p Fo(E)6 b Fp(\))28 b(=)g Fo(\025)p Fp(\()o Fo(E)6 b Fp(\))p Fo(:)984 b Fp(\(2.4\))386 1445 y(It)35 b(ma)m(y)i(also)e(b)s (e)h(assumed)h(that)e Fo(v)t Fp(\()p Fo(E)6 b Fp(\))35 b(is)h(the)g(\014rst)g(ro)m(w)g(of)f Fo(T)14 b Fp(\()o Fo(E)6 b Fp(\))2895 1396 y Fn(\000)p Fj(1)2990 1445 y Fp(.)52 b(Clearly)386 1561 y(b)m(y)35 b(\(2.4\))d Fo(\014)817 1525 y Fm(s)811 1586 y Fj(1)853 1561 y Fp(\()p Fo(E)6 b Fp(\))33 b(is)g(smo)s(oth)f(for)g Fo(E)i Fk(2)28 b Fo(I)1874 1576 y Fj(0)1914 1561 y Fp(.)486 1677 y(W)-8 b(e)42 b(call)h Fo(E)924 1692 y Fj(0)1006 1677 y Fp(a)f(resonance)i(of) e(order)h Fo(m)i Fk(2)g(f)p Fp(2)p Fo(;)17 b Fp(3)p Fo(;)g(:)g(:)g(:)e Fk(g)42 b Fp(for)g(an)g(eigen)m(v)-5 b(alue)386 1804 y Fo(\014)447 1757 y Fj(#)441 1829 y Fm(j)509 1804 y Fp(\()p Fo(E)619 1819 y Fj(0)659 1804 y Fp(\))33 b(if)f(for)g(some)h Fo(\013)c Fp(=)e(\()p Fo(\013)1506 1819 y Fj(1)1546 1804 y Fo(;)17 b(:)g(:)g(:)f(\013)1783 1819 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)1955 1804 y Fp(\))28 b Fk(2)g Fp(\()p FC(N)p Fk([f)o Fp(0)p Fk(g)p Fp(\))2493 1755 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)2698 1804 y Fp(with)33 b Fk(j)p Fo(\013)q Fk(j)27 b Fp(=)g Fo(m)p Fp(,)1454 1987 y Fo(\014)1515 1940 y Fj(#)1509 2013 y Fm(j)1578 1987 y Fp(\()p Fo(E)1688 2002 y Fj(0)1727 1987 y Fp(\))h(=)g Fo(\014)6 b Fp(\()o Fo(E)2067 2002 y Fj(0)2107 1987 y Fp(\))22 b Fk(\001)g Fo(\013)q(:)867 b Fp(\(2.5\))486 2146 y(W)-8 b(e)33 b(assume)h(that)813 2305 y Fo(E)885 2320 y Fj(0)952 2305 y Fo(is)28 b(not)g(a)g(r)s (esonance)g(of)39 b(or)s(der)57 b Fk(\024)28 b Fo(m)2388 2320 y Fj(0)2456 2305 y Fo(f)11 b(or)30 b(\014)2697 2264 y Fm(s)2691 2330 y Fj(1)2733 2305 y Fp(\()p Fo(E)2843 2320 y Fj(0)2883 2305 y Fp(\))p Fo(:)229 b Fp(\(H8\))386 2465 y(Here)33 b Fo(m)701 2480 y Fj(0)773 2465 y Fp(ma)m(y)h(b)s(e)f (extracted)g(from)g(the)g(bulk)g(of)f(the)h(pap)s(er;)g(the)g (condition)624 2680 y Fo(m)709 2695 y Fj(0)776 2680 y Fo(>)28 b Fp(max)1078 2539 y Fi(\022)1151 2680 y Fp(4)p Fo(;)1254 2612 y Fp(1)22 b(+)g(Re)16 b(\()p Fo(\014)1653 2576 y Fm(s)1647 2637 y Fj(1)1690 2612 y Fp(\()p Fo(E)1800 2627 y Fj(0)1839 2612 y Fp(\)\))p 1254 2657 662 4 v 1291 2748 a Fk(\000)h Fp(Re)g(\()p Fo(\014)1616 2714 y Fm(s)1610 2772 y Fj(1)1652 2748 y Fp(\()p Fo(E)1762 2763 y Fj(0)1802 2748 y Fp(\)\))1925 2680 y Fo(;)g(:)g(:)g(:)f(;)2154 2612 y Fp(1)22 b(+)g(Re)16 b(\()p Fo(\014)2553 2576 y Fm(s)2547 2637 y(n)2590 2618 y Ff(s)2628 2612 y Fp(\()o Fo(E)2737 2627 y Fj(0)2777 2612 y Fp(\)\))p 2154 2657 700 4 v 2191 2748 a Fk(\000)h Fp(Re)g(\()p Fo(\014)2516 2714 y Fm(s)2510 2770 y(n)2553 2751 y Ff(s)2590 2748 y Fp(\()p Fo(E)2700 2763 y Fj(0)2740 2748 y Fp(\)\))2863 2539 y Fi(\023)3174 2680 y Fp(\(2.6\))386 2895 y(su\016ces.)386 3070 y Fg(R)-5 b(emark)56 b Fp(2.1)p Fg(.)48 b Fp(The)d(theorem)h(pro)m (v)m(ed)g(with)g(\(H8\))e(do)s(es)i(not)e(exclude)j(cases)386 3187 y(where)35 b(there)h(are)e(lo)m(w)h(order)f(resonances)i(as)f (long)f(as)h(they)g(constitute)g(a)f(dis-)386 3303 y(crete)27 b(set.)42 b(This)28 b(is)f(used)g(in)g(the)g(pro)s(of)e(of)h(Theorem)i (1.2)e(in)g(Section)i(8.)41 b(F)-8 b(or)25 b(the)386 3419 y(exceptional)i(v)-5 b(alues)26 b Fo(a)i Fp(=)1366 3380 y Fj(3)p 1366 3396 36 4 v 1366 3454 a(4)1437 3419 y Fp(and)d Fo(a)j Fp(=)f(2)e(of)g(Example)i(1.3)e(there)h(are)f (resonances)386 3535 y(of)i(order)g(5)h(and)f(4,)h(resp)s(ectiv)m(ely) -8 b(.)45 b(F)-8 b(or)27 b(these)h(v)-5 b(alues)29 b(of)e Fo(a)g Fg(al)5 b(l)27 b Fp(p)s(ositiv)m(e)i(energies)386 3652 y(are)k(resonances,)h(and)f(consequen)m(tly)i(our)e(theorem)g(is)g (not)g(applicable.)486 3827 y(W)-8 b(e)42 b(shall)h(build)g(a)f (\(classical\))i(observ)-5 b(able)43 b(\000)f(from)g(the)h(\014rst)g (co)s(ordinate)386 3944 y Fo(\015)437 3959 y Fj(1)504 3944 y Fp(=)27 b Fo(\015)658 3959 y Fj(1)697 3944 y Fp(\()p Fo(w)s Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(E)6 b Fp(\))28 b(=)f Fo(v)t Fp(\()p Fo(E)6 b Fp(\))22 b Fk(\001)g Fo(w)s Fp(\()o Fo(E)6 b Fp(\))33 b(of)f Fo(\015)1955 3907 y Fm(s)2019 3944 y Fp(=)c Fo(\015)2179 3907 y Fm(s)2216 3944 y Fp(\()p Fo(w)s Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(E)6 b Fp(\))1082 4104 y(\000)28 b(=)f Fo(\015)1325 4119 y Fj(1)1364 4104 y Fp(\()p Fo(w)s Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(E)6 b Fp(\))22 b(+)g Fo(O)1986 4024 y Fi(\000)2031 4104 y Fk(j)p Fo(\015)5 b Fp(\()p Fo(w)s Fp(\()o Fo(E)h Fp(\))p Fo(;)17 b(E)6 b Fp(\))p Fk(j)2567 4063 y Fj(2)2606 4024 y Fi(\001)2652 4104 y Fo(:)495 b Fp(\(2.7\))486 4264 y(In)47 b(the)g(study)h(of)e(an)h(analogous)f (quan)m(tum)j(observ)-5 b(able)47 b(w)m(e)h(consider)g(in)386 4380 y(detail)33 b(the)g(case)g(where)h(for)e(some)i(1)27 b Fk(\024)h Fo(l)i Fk(\024)e Fo(n)23 b Fk(\000)f Fp(1)1439 4539 y Fo(@)1490 4554 y Fm(\021)1525 4566 y Ff(l)1554 4539 y Fo(\015)1605 4554 y Fj(1)1644 4539 y Fp(\()p Fo(w)s(;)17 b(E)1871 4554 y Fj(0)1910 4539 y Fp(\))1948 4568 y Fn(j)p Fm(w)r Fj(=0)2142 4539 y Fk(6)p Fp(=)28 b(0)p Fo(:)852 b Fp(\(2.8\))386 4711 y(W)-8 b(e)33 b(notice)g(that)f(if)h(\(2.8\))f (is)h(not)f(true)h(then)h(for)e(some)h(1)27 b Fk(\024)i Fo(l)h Fk(\024)e Fo(n)22 b Fk(\000)h Fp(1)1436 4870 y Fo(@)1487 4885 y Fm(u)1528 4897 y Ff(l)1557 4870 y Fo(\015)1608 4885 y Fj(1)1647 4870 y Fp(\()p Fo(w)s(;)17 b(E)1874 4885 y Fj(0)1913 4870 y Fp(\))1951 4899 y Fn(j)p Fm(w)r Fj(=0)2145 4870 y Fk(6)p Fp(=)27 b(0)p Fo(:)850 b Fp(\(2.9\))486 5042 y(The)32 b(construction)g(of)f(the)g(quan)m(tum)i(\000)e(in)g(the) h(case)g(of)f(\(2.8\))f(and)i(an)f(elab-)386 5158 y(oration)40 b(of)g(its)h(deca)m(y)h(prop)s(erties)g(will)f(b)s(e)g(giv)m(en)h(in)f (Section)g(5.)67 b(A)41 b(Mourre)386 5274 y(esimate)26 b(is)g(giv)m(en)g(in)f(Section)h(6,)h(and)e(w)m(e)h(complete)g(the)g (pro)s(of)e(of)h(Theorem)h(1.1)386 5390 y(in)34 b(this)h(case)f(in)h (Section)f(7.)47 b(W)-8 b(e)35 b(refer)f(the)g(reader)h(to)e(Remarks)i (5.3,)f(6.3)g(and)386 5506 y(7.2)i(for)g(the)h(mo)s(di\014cations)h (needed)g(for)e(sho)m(wing)i(Theorem)g(1.1)e(in)h(the)g(case)386 5623 y(of)32 b(\(2.9\).)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 386 259 a Fl(12)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y Fp(2.1.)48 b FC(Outline)f(of)g(pro)s(of)g(of)f(Theorem)h(1.1.)i Fp(Consider)42 b(a)e(classical)i(orbit)386 575 y(with)34 b(\()6 b(^)-55 b Fo(x)q Fp(\()p Fo(t)p Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(t)p Fp(\)\))30 b Fk(!)g Fp(\()p Fo(!)t Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(\030)5 b Fp(\()o Fo(E)h Fp(\)\))34 b(for)f Fo(t)d Fk(!)g(1)j Fp(\(and)h Fo(E)40 b Fp(nearb)m(y)35 b Fo(E)2999 590 y Fj(0)3073 575 y Fp(\).)47 b(Ho)m(w)386 691 y(do)32 b(w)m(e)i(pro)m(v)m(e)g(the)f (b)s(ound)g Fk(j)p Fo(u)p Fk(j)21 b Fp(+)h Fk(j)p Fo(\021)t Fk(j)k(\024)j Fo(C)7 b(t)1980 655 y Fn(\000)p Fm(\016)2105 691 y Fp(for)32 b(some)h(p)s(ositiv)m(e)h Fo(\016)t Fp(?)486 807 y(W)-8 b(e)33 b(consider)g(the)g(observ)-5 b(ables)518 970 y Fo(q)565 929 y Fm(s)630 970 y Fp(=)27 b Fk(j)p Fo(\015)817 929 y Fm(s)854 970 y Fk(j)882 929 y Fj(2)921 970 y Fo(;)65 b(q)1060 929 y Fm(u)1133 970 y Fp(=)27 b Fk(j)p Fo(\015)1320 929 y Fm(u)1365 970 y Fk(j)1393 929 y Fj(2)1432 970 y Fo(;)66 b(q)1572 929 y Fn(\000)1658 970 y Fp(=)28 b Fo(q)1809 929 y Fm(u)1876 970 y Fk(\000)22 b Fo(q)2022 929 y Fm(s)2059 970 y Fo(;)65 b(q)2198 929 y Fj(+)2285 970 y Fp(=)27 b Fo(q)2435 929 y Fm(u)2502 970 y Fp(+)22 b Fo(q)2647 929 y Fm(s)2712 970 y Fp(=)27 b Fk(j)p Fo(\015)5 b Fk(j)2927 929 y Fj(2)2966 970 y Fo(:)132 b Fp(\(2.10\))486 1133 y(Using)34 b(\(1.6\))e(and)h(\(2.1\))f (w)m(e)h(compute)975 1282 y Fo(d)p 957 1326 86 4 v 957 1418 a(dt)1053 1349 y(\015)g Fp(=)1250 1282 y Fo(@)1301 1297 y Fm(\026)1348 1282 y Fo(h)p 1250 1326 155 4 v 1276 1418 a(x)1331 1433 y Fm(n)1414 1269 y Fi(\010)1472 1349 y Fp(\()p Fo(B)1589 1308 y Fm(s)1626 1349 y Fp(\()p Fo(E)6 b Fp(\))p Fo(\015)1836 1308 y Fm(s)1873 1349 y Fo(;)17 b(B)1996 1308 y Fm(u)2041 1349 y Fp(\()p Fo(E)6 b Fp(\))p Fo(\015)2251 1308 y Fm(u)2296 1349 y Fp(\))22 b(+)g Fo(O)2532 1269 y Fi(\000)2577 1349 y Fo(q)2624 1308 y Fj(+)2683 1269 y Fi(\001)o(\011)2786 1349 y Fo(:)312 b Fp(\(2.11\))486 1562 y(F)-8 b(or)31 b Fo(\017)d(>)g Fp(0)k(small)h(enough)g(in)g (\(2.2\))f(the)h(equation)h(\(2.11\))d(leads)j(to)481 1719 y Fo(d)p 464 1763 86 4 v 464 1855 a(dt)560 1786 y(q)607 1745 y Fn(\000)693 1786 y Fp(=)28 b(2)17 b(Re)994 1646 y Fi(\034)1069 1786 y Fo(\015)1125 1745 y Fm(u)1170 1786 y Fo(;)1241 1719 y(d)p 1223 1763 V 1223 1855 a(dt)1319 1786 y(\015)1375 1745 y Fm(u)1420 1646 y Fi(\035)1495 1885 y Fd(C)1554 1866 y Ff(n)1592 1852 y(u)1663 1786 y Fk(\000)23 b Fp(2)17 b(Re)1960 1646 y Fi(\034)2035 1786 y Fo(\015)2091 1745 y Fm(s)2128 1786 y Fo(;)2199 1719 y(d)p 2181 1763 V 2181 1855 a(dt)2277 1786 y(\015)2333 1745 y Fm(s)2370 1646 y Fi(\035)2445 1885 y Fd(C)2504 1866 y Ff(n)2542 1852 y(s)2611 1786 y Fk(\025)28 b Fo(\016)2763 1745 y Fn(\000)2822 1786 y Fo(t)2857 1745 y Fn(\000)p Fj(1)2952 1786 y Fo(q)2999 1745 y Fj(+)3125 1786 y Fp(\(2.12\))386 2016 y(for)45 b(some)i(p)s(ositiv)m(e)g Fo(\016)1227 1980 y Fn(\000)1332 2016 y Fp(\(whic)m(h)h(ma)m(y)e(b)s(e)h(c)m(hosen)g (indep)s(enden)m(t)h(of)e Fo(E)52 b Fp(close)386 2132 y(enough)33 b(to)f Fo(E)913 2147 y Fj(0)953 2132 y Fp(\))g(and)h(for)f (all)g Fo(t)c Fk(\025)h Fo(t)1701 2096 y Fn(\000)1792 2132 y Fp(\(with)k Fo(t)2087 2096 y Fn(\000)2179 2132 y Fp(large)g(enough\).)486 2249 y(In)f(particular)h Fo(q)1104 2212 y Fn(\000)1196 2249 y Fp(is)g(increasing)h(and)e(hence)1521 2411 y Fo(q)1568 2370 y Fn(\000)1655 2411 y Fk(\024)c Fp(0;)114 b Fo(t)28 b Fk(\025)g Fo(t)2153 2370 y Fn(\000)2212 2411 y Fo(:)886 b Fp(\(2.13\))486 2574 y(Using)30 b(\(2.11\),)g (\(2.13\))g(and)g(the)h(Cauc)m(h)m(y-Sc)m(h)m(w)m(arz)i(inequalit)m(y)f (w)m(e)g(compute)1059 2731 y Fo(d)p 1042 2775 V 1042 2867 a(dt)1138 2798 y(q)1185 2757 y Fm(s)1249 2798 y Fp(=)27 b(2)17 b(Re)1550 2658 y Fi(\034)1624 2798 y Fo(\015)1680 2757 y Fm(s)1717 2798 y Fo(;)1788 2731 y(d)p 1771 2775 V 1771 2867 a(dt)1867 2798 y(\015)1923 2757 y Fm(s)1959 2658 y Fi(\035)2034 2897 y Fd(C)2093 2878 y Ff(n)2131 2864 y(s)2201 2798 y Fk(\024)28 b(\000)p Fp(2)p Fo(\016)2479 2757 y Fm(s)2516 2798 y Fo(t)2551 2757 y Fn(\000)p Fj(1)2645 2798 y Fo(q)2692 2757 y Fm(s)3125 2798 y Fp(\(2.14\))386 3021 y(for)k(some)h(p)s(ositiv)m(e)h Fo(\016)1187 2985 y Fm(s)1257 3021 y Fp(and)e(all)h Fo(t)28 b Fk(\025)g Fo(t)1785 2985 y Fm(s)1822 3021 y Fp(.)486 3137 y(In)m(tegrating)33 b(\(2.14\))e(yields)1413 3304 y Fo(q)1460 3263 y Fm(s)1524 3304 y Fk(\024)d Fo(C)1706 3263 y Fm(s)1743 3304 y Fo(t)1778 3263 y Fn(\000)p Fj(2)p Fm(\016)1901 3240 y Ff(s)1939 3304 y Fo(;)115 b(t)28 b Fk(\025)g Fo(t)2284 3263 y Fm(s)2321 3304 y Fo(:)777 b Fp(\(2.15\))486 3467 y(Finally)35 b(from)g(\(2.13\))f (and)h(\(2.15\))f(w)m(e)i(conclude)h(that)e Fo(q)2624 3431 y Fj(+)2714 3467 y Fk(\024)e Fp(2)p Fo(C)2950 3431 y Fm(s)2986 3467 y Fo(t)3021 3431 y Fn(\000)p Fj(2)p Fm(\016)3144 3407 y Ff(s)3218 3467 y Fp(and)386 3583 y(therefore)g(that)1440 3705 y Fk(j)p Fo(\015)5 b Fk(j)27 b(\024)h Fo(C)7 b(t)1796 3664 y Fn(\000)p Fm(\016)1889 3705 y Fp(;)114 b Fo(\016)32 b Fk(\024)c Fo(\016)2257 3664 y Fm(s)2294 3705 y Fo(:)804 b Fp(\(2.16\))386 3883 y Fg(R)-5 b(emarks)42 b Fp(2.2)p Fg(.)534 4022 y Fp(\(1\))f(W)-8 b(e)47 b(ma)m(y)h(c)m(ho)s(ose)f(the)g(p)s(ositiv)m(e)h Fo(\016)i Fp(in)d(\(2.16\))f(as)h(close)g(to)f(the)h(\(op-)700 4139 y(timal\))e(exp)s(onen)m(t)g(min)18 b(\(Re)e(\()p Fk(\000)p Fo(\014)1961 4103 y Fm(s)1955 4163 y Fj(1)1998 4139 y Fp(\()p Fo(E)2108 4154 y Fj(0)2148 4139 y Fp(\)\))p Fo(;)h(:)g(:)g(:)e(;)i Fp(Re)g(\()p Fk(\000)p Fo(\014)2750 4103 y Fm(s)2744 4163 y(n)2787 4144 y Ff(s)2825 4139 y Fp(\()p Fo(E)2935 4154 y Fj(0)2974 4139 y Fp(\)\)\))44 b(as)h(w)m(e)700 4255 y(wish)34 b(\(pro)m(vided)g Fo(E)39 b Fp(is)33 b(tak)m(en)g(close)h(enough)f(to)f Fo(E)2597 4270 y Fj(0)2637 4255 y Fp(\).)534 4371 y(\(2\))41 b(Although)h(not)e (needed,)45 b(one)c(ma)m(y)h(easily)g(pro)m(v)m(e)g(using)g(similar)f (dif-)700 4496 y(feren)m(tial)49 b(inequalities)i(that)c(indeed)j Fo(q)2222 4459 y Fm(u)2321 4496 y Fp(=)k Fo(O)2529 4415 y Fi(\000)2573 4496 y Fp(\()p Fo(q)2658 4459 y Fm(s)2695 4496 y Fp(\))2733 4447 y Fj(2)2772 4415 y Fi(\001)2866 4496 y Fp(in)48 b(complete)700 4612 y(agreemen)m(t)34 b(with)f(the)g(stable)h(manifold)f(theorem.)386 4790 y(2.2.)48 b FC(Classical)40 b Fp(\000)p FC(.)49 b Fp(W)-8 b(e)33 b(shall)h(for)e(eac)m(h)i Fo(m)29 b Fk(2)g(f)p Fp(1)p Fo(;)17 b(:)g(:)g(:)e(;)i(m)2564 4805 y Fj(0)2604 4790 y Fk(g)32 b Fp(construct)i(a)f Fo(\015)3253 4753 y Fj(\()q Fm(m)p Fj(\))386 4906 y Fp(of)f(the)h(form)f(\(2.7\))g(suc)m (h)i(that)691 5055 y Fo(d)p 673 5099 V 673 5190 a(dt)769 5122 y(\015)825 5081 y Fj(\()q Fm(m)p Fj(\))974 5122 y Fp(=)1088 5055 y Fo(@)1139 5070 y Fm(\026)1186 5055 y Fo(h)p 1088 5099 155 4 v 1114 5190 a(x)1169 5205 y Fm(n)1252 5122 y Fo(\014)1313 5081 y Fm(s)1307 5147 y Fj(1)1349 5041 y Fi(\010)1407 5122 y Fo(\015)1463 5081 y Fj(\()q Fm(m)p Fj(\))1607 5122 y Fp(+)22 b Fo(O)1783 5041 y Fi(\000)1828 5122 y Fk(j)p Fo(\015)5 b Fk(j)1940 5081 y Fm(m)p Fj(+1)2096 5041 y Fi(\001\011)2200 5122 y Fp(;)114 b Fo(\014)2402 5081 y Fm(s)2396 5147 y Fj(1)2466 5122 y Fp(=)28 b Fo(\014)2631 5081 y Fm(s)2625 5147 y Fj(1)2667 5122 y Fp(\()p Fo(E)6 b Fp(\))p Fo(:)277 b Fp(\(2.17\))386 5329 y(Sp)s(eci\014cally)34 b(w)m(e)g(shall)f(require) 707 5508 y Fo(\015)763 5467 y Fj(\()q(1\))885 5508 y Fp(=)28 b Fo(\015)1040 5523 y Fj(1)1079 5508 y Fo(;)49 b Fp(and)33 b Fo(\015)1401 5467 y Fj(\()p Fm(m)p Fj(\))1550 5508 y Fp(=)27 b Fo(\015)1704 5523 y Fj(1)1765 5508 y Fp(+)1937 5413 y Fi(X)1863 5629 y Fj(2)p Fn(\024j)p Fm(\013)p Fn(j\024)p Fm(m)2172 5508 y Fo(c)2214 5523 y Fm(\013)2264 5508 y Fo(\015)2320 5467 y Fm(\013)2369 5508 y Fp(;)114 b Fo(m)28 b Fk(\025)g Fp(2)p Fo(;)321 b Fp(\(2.18\))p eop end %%Page: 13 13 TeXDict begin 13 12 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(13)386 459 y Fp(with)41 b Fo(\015)672 423 y Fm(\013)762 459 y Fp(=)f Fo(\015)934 415 y Fm(\013)979 424 y Fh(1)929 483 y Fj(1)1035 459 y Fk(\001)17 b(\001)g(\001)e Fo(\015)1224 408 y Fm(\013)1269 417 y Fh(2)p Ff(n)p Fc(\000)p Fh(2)1219 483 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)1425 459 y Fp(.)66 b(\(It)40 b(will)h(follo)m(w)g(from)f(the)g(construction)i(b) s(elo)m(w)386 575 y(that)31 b(the)h(co)s(e\016cien)m(ts)i Fo(c)1298 590 y Fm(\013)1375 575 y Fp(=)28 b Fo(c)1521 590 y Fm(\013)1570 575 y Fp(\()p Fo(E)6 b Fp(\))32 b(will)g(b)s(e)g (smo)s(oth;)g(this)g(will)h(b)s(e)f(imp)s(ortan)m(t)386 691 y(for)g(\\quan)m(tizing")h(the)g(sym)m(b)s(ol.\))486 807 y(W)-8 b(e)31 b(pro)s(ceed)g(inductiv)m(ely)-8 b(.)45 b(Clearly)32 b(b)m(y)g(\(2.11\))e(w)m(e)h(ha)m(v)m(e)h(\(2.17\))e(for)g Fo(m)e Fp(=)g(1.)386 927 y(No)m(w)36 b(supp)s(ose)g(w)m(e)h(ha)m(v)m(e) f(constructed)h(a)e(function)h Fo(\015)2408 890 y Fj(\()p Fm(m)p Fn(\000)p Fj(1\))2652 927 y Fp(=)2760 852 y Fi(P)2865 956 y Fn(j)p Fm(\013)p Fn(j\024)p Fm(m)p Fn(\000)p Fj(1)3178 927 y Fo(c)3220 942 y Fm(\013)3269 927 y Fo(\015)3325 890 y Fm(\013)386 1050 y Fp(ob)s(eying)748 1196 y Fo(d)p 731 1241 86 4 v 731 1332 a(dt)827 1264 y(\015)883 1222 y Fj(\()p Fm(m)p Fn(\000)p Fj(1\))1122 1264 y Fp(=)1236 1196 y Fo(@)1287 1211 y Fm(\026)1334 1196 y Fo(h)p 1236 1241 155 4 v 1262 1332 a(x)1317 1347 y Fm(n)1400 1264 y Fo(\014)1461 1222 y Fm(s)1455 1288 y Fj(1)1497 1123 y Fi(\022)1571 1264 y Fo(\015)1627 1222 y Fj(\()p Fm(m)p Fn(\000)p Fj(1\))1860 1264 y Fp(+)1987 1169 y Fi(X)1958 1385 y Fn(j)p Fm(\013)p Fn(j)p Fj(=)p Fm(m)2177 1264 y Fo(d)2228 1279 y Fm(\013)2277 1264 y Fo(\015)2333 1222 y Fm(\013)2405 1264 y Fp(+)22 b Fo(O)2581 1183 y Fi(\000)2626 1264 y Fk(j)o Fo(\015)5 b Fk(j)2737 1215 y Fm(m)p Fj(+1)2894 1183 y Fi(\001)2939 1123 y(\023)3013 1264 y Fo(;)386 1547 y Fp(then)30 b(w)m(e)g(add)f(to)g Fo(\015)1103 1511 y Fj(\()p Fm(m)p Fn(\000)p Fj(1\))1344 1547 y Fp(a)g(function)g(of)g (the)g(form)2299 1473 y Fi(P)2405 1576 y Fn(j)o Fm(\013)p Fn(j)p Fj(=)p Fm(m)2627 1547 y Fo(c)2669 1562 y Fm(\013)2719 1547 y Fo(\015)2775 1511 y Fm(\013)2853 1547 y Fp(and)g(w)m(e)i(need) 386 1671 y(to)h(solv)m(e)656 1790 y Fo(d)p 638 1834 86 4 v 638 1926 a(dt)780 1763 y Fi(X)751 1978 y Fn(j)p Fm(\013)p Fn(j)o Fj(=)p Fm(m)969 1857 y Fo(c)1011 1872 y Fm(\013)1061 1857 y Fo(\015)1117 1816 y Fm(\013)1194 1857 y Fp(=)1308 1790 y Fo(@)1359 1805 y Fm(\026)1406 1790 y Fo(h)p 1308 1834 155 4 v 1333 1926 a(x)1388 1941 y Fm(n)1472 1857 y Fo(\014)1533 1816 y Fm(s)1527 1882 y Fj(1)1615 1763 y Fi(X)1586 1978 y Fn(j)o Fm(\013)p Fn(j)p Fj(=)p Fm(m)1804 1857 y Fp(\()p Fo(c)1884 1872 y Fm(\013)1956 1857 y Fk(\000)22 b Fo(d)2106 1872 y Fm(\013)2155 1857 y Fp(\))p Fo(\015)2249 1816 y Fm(\013)2321 1857 y Fp(+)g Fo(O)2497 1776 y Fi(\000)2542 1857 y Fk(j)p Fo(\015)5 b Fk(j)2653 1809 y Fm(m)p Fj(+1)2810 1776 y Fi(\001)2856 1857 y Fo(:)242 b Fp(\(2.19\))486 2130 y(F)-8 b(or)25 b(that)g(w)m(e)i(compute)h(the)e(deriv)-5 b(ativ)m(e)27 b(using)g(again)f(\(2.11\).)40 b(Let)26 b(us)h(denote)386 2252 y(b)m(y)49 b Fo(\014)592 2267 y Fm(ij)701 2252 y Fp(the)g Fo(ij)6 b Fp('th)49 b(en)m(try)g(of)f(the)h (matrix)g(diag)2225 2172 y Fi(\000)2270 2252 y Fo(B)2349 2216 y Fm(s)2386 2252 y Fp(\()p Fo(E)6 b Fp(\))2540 2204 y Fm(tr)2604 2252 y Fo(;)17 b(B)2727 2216 y Fm(u)2772 2252 y Fp(\()p Fo(E)6 b Fp(\))2925 2204 y Fm(tr)2989 2172 y Fi(\001)3035 2252 y Fp(.)91 b(Then)386 2370 y(\(2.19\))32 b(reduces)i(to)e(solving)784 2455 y Fi(X)755 2671 y Fn(j)7 b Fj(~)-42 b Fm(\013)p Fn(j)p Fj(=)p Fm(m)973 2455 y Fi(X)1007 2665 y Fm(i;j)1144 2550 y Fp(~)-59 b Fo(\013)1196 2565 y Fm(i)1224 2550 y Fo(\014)1279 2565 y Fm(ij)1340 2550 y Fo(c)1389 2565 y Fj(~)-42 b Fm(\013)1431 2550 y Fo(\015)1494 2509 y Fj(~)g Fm(\013)q Fn(\000)p Fm(e)1621 2519 y Ff(i)1647 2509 y Fj(+)p Fm(e)1735 2519 y Ff(j)1799 2550 y Fp(=)27 b Fo(\014)1963 2509 y Fm(s)1957 2574 y Fj(1)2045 2455 y Fi(X)2016 2671 y Fn(j)p Fm(\013)p Fn(j)p Fj(=)p Fm(m)2234 2550 y Fp(\()p Fo(c)2314 2565 y Fm(\013)2386 2550 y Fk(\000)c Fo(d)2537 2565 y Fm(\013)2586 2550 y Fp(\))p Fo(\015)2680 2509 y Fm(\013)2729 2550 y Fo(;)369 b Fp(\(2.20\))386 2817 y(whic)m(h)34 b(in)f(turn)g(reduces)h(to)e (solving)i(the)f(system)h(of)e(algebraic)h(equations)614 2896 y Fi(X)648 3106 y Fm(i;j)775 2991 y Fp(\()p Fo(\013)875 3006 y Fm(i)925 2991 y Fp(+)22 b(1)g Fk(\000)h Fo(\016)1237 3006 y Fm(ij)1297 2991 y Fp(\))p Fo(\014)1390 3006 y Fm(ij)1451 2991 y Fo(c)1493 3006 y Fm(\013)p Fj(+)p Fm(e)1626 3016 y Ff(i)1652 3006 y Fn(\000)p Fm(e)1740 3016 y Ff(j)1804 2991 y Fp(=)28 b Fo(\014)1969 2950 y Fm(s)1963 3015 y Fj(1)2005 2991 y Fp(\()p Fo(c)2085 3006 y Fm(\013)2157 2991 y Fk(\000)22 b Fo(d)2307 3006 y Fm(\013)2356 2991 y Fp(\);)115 b Fk(j)p Fo(\013)q Fk(j)26 b Fp(=)i Fo(m:)228 b Fp(\(2.21\))386 3258 y(Here)39 b Fo(e)667 3273 y Fm(i)733 3258 y Fp(and)g Fo(e)974 3273 y Fm(j)1049 3258 y Fp(denote)g(canonical) g(basis)g(v)m(ectors)h(in)e FC(R)2588 3222 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)2798 3258 y Fp(and)h Fo(\016)3037 3273 y Fm(ij)3135 3258 y Fp(is)g(the)386 3374 y(Kronec)m(k)m(er)34 b(sym)m(b)s(ol.)486 3490 y(Clearly)42 b(\(2.21\))e(amoun)m(ts)h(to)g (sho)m(wing)h(that)f Fo(\014)2313 3454 y Fm(s)2307 3515 y Fj(1)2390 3490 y Fp(is)g(not)g(an)g(eigen)m(v)-5 b(alue)42 b(of)386 3615 y(the)33 b(linear)g(map)1065 3590 y(~)1042 3615 y Fo(B)k Fp(on)c FC(C)1374 3579 y Fj(~)-39 b Fm(n)1449 3615 y Fp(with)725 3826 y(~)-53 b Fo(n)28 b Fp(=)f(#)991 3746 y Fi(\010)1050 3826 y Fo(\013)h Fk(2)g Fp(\()p FC(N)p Fk([f)p Fp(0)p Fk(g)o Fp(\))1612 3778 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)1785 3826 y Fk(j)97 b(j)p Fo(\013)q Fk(j)27 b Fp(=)g Fo(m)2244 3746 y Fi(\011)2330 3826 y Fp(=)2444 3759 y(\()p Fo(m)22 b Fp(+)g(2)p Fo(n)g Fk(\000)h Fp(3\)!)p 2444 3804 586 4 v 2490 3895 a(\(2)p Fo(n)g Fk(\000)f Fp(3\)!)p Fo(m)p Fp(!)386 4039 y(giv)m(en)34 b(b)m(y)469 4226 y FC(C)554 4185 y Fj(~)-39 b Fm(n)625 4226 y Fk(3)28 b Fo(c)f Fp(=)h(\()p Fo(c)972 4241 y Fm(\013)1021 4226 y Fp(\))1059 4255 y Fm(\013)1119 4447 y Fk(!)1247 4366 y Fi(\000)1316 4422 y Fp(~)1292 4447 y Fo(B)6 b(c)1414 4366 y Fi(\001)1459 4486 y Fm(\013)1536 4447 y Fp(=)1640 4306 y Fi(\022)1730 4352 y(X)1764 4562 y Fm(i;j)1890 4447 y Fp(\()p Fo(\013)1990 4462 y Fm(i)2041 4447 y Fp(+)22 b(1)g Fk(\000)g Fo(\016)2352 4462 y Fm(ij)2413 4447 y Fp(\))p Fo(\014)2506 4462 y Fm(ij)2567 4447 y Fo(c)2609 4462 y Fm(\013)p Fj(+)p Fm(e)2742 4472 y Ff(i)2768 4462 y Fn(\000)p Fm(e)2856 4472 y Ff(j)2892 4306 y Fi(\023)2965 4546 y Fm(\013)3043 4447 y Fk(2)28 b FC(C)3222 4406 y Fj(~)-39 b Fm(n)3265 4447 y Fo(:)386 4710 y Fp(Since)41 b Fo(\014)703 4725 y Fm(ij)804 4710 y Fp(=)g Fo(\014)976 4725 y Fm(ij)1036 4710 y Fp(\()p Fo(E)6 b Fp(\))40 b(dep)s(ends)i(con)m (tin)m(uously)g(on)e Fo(E)47 b Fk(2)41 b Fo(I)2601 4725 y Fj(0)2680 4710 y Fp(w)m(e)g(only)g(need)g(to)386 4826 y(sho)m(w)34 b(that)1264 4918 y(~)1240 4943 y Fo(B)5 b Fp(\()p Fo(E)1429 4958 y Fj(0)1469 4943 y Fp(\))22 b Fk(\000)h Fo(\014)1690 4902 y Fm(s)1684 4968 y Fj(1)1726 4943 y Fp(\()p Fo(E)1836 4958 y Fj(0)1876 4943 y Fp(\))p Fo(I)40 b Fp(is)33 b(in)m(v)m(ertible.)607 b(\(2.22\))386 5081 y(By)31 b(the)g(condition)g(\(H8\))f(indeed)i(\(2.22\))d(holds)i (since)h Fo(m)c Fk(\024)h Fo(m)2737 5096 y Fj(0)2807 5081 y Fp(and)h(the)h(sp)s(ec-)386 5197 y(trum)1108 5321 y Fo(\033)1167 5210 y Fi(\020)1250 5296 y Fp(~)1226 5321 y Fo(B)5 b Fp(\()p Fo(E)1415 5336 y Fj(0)1455 5321 y Fp(\))1493 5210 y Fi(\021)1580 5321 y Fp(=)28 b Fk(f)o Fo(\014)6 b Fp(\()p Fo(E)1904 5336 y Fj(0)1944 5321 y Fp(\))22 b Fk(\001)g Fo(\013)q Fk(j)96 b(j)p Fo(\013)q Fk(j)27 b Fp(=)h Fo(m)p Fk(g)p Fo(:)386 5505 y Fp(The)c(latter)g(is)g (ob)m(vious)h(if)e(diag)1544 5424 y Fi(\000)1589 5505 y Fo(B)1668 5469 y Fm(s)1705 5505 y Fp(\()p Fo(E)1815 5520 y Fj(0)1855 5505 y Fp(\))1893 5456 y Fm(tr)1956 5505 y Fo(;)17 b(B)2079 5469 y Fm(u)2124 5505 y Fp(\()p Fo(E)2234 5520 y Fj(0)2274 5505 y Fp(\))2312 5456 y Fm(tr)2375 5424 y Fi(\001)2444 5505 y Fp(is)24 b(diagonal.)40 b(In)24 b(general)386 5623 y(this)33 b(ma)m(y)g(b)s(e)g(seen)h(b)m(y)g(a)e(p)s (erturbation)h(argumen)m(t,)g(see)h([N,)f(p.)43 b(37].)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 386 259 a Fl(14)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)486 459 y Fp(Finally)32 b(w)m(e)i(de\014ne)1665 586 y(\000)27 b(=)h Fo(\015)1913 545 y Fj(\()p Fm(m)2002 554 y Fh(0)2037 545 y Fj(\))2069 586 y Fo(:)486 731 y Fp(If)j(w)m(e)h(ha)m(v)m(e)h Fo(m)1033 746 y Fj(0)1104 731 y Fp(so)f(large)f(that)g Fo(\016)t Fp(\()p Fo(m)1840 746 y Fj(0)1902 731 y Fp(+)22 b(1\))27 b Fo(>)h Fk(\000)p Fo(\014)2356 694 y Fm(s)2350 755 y Fj(1)2393 731 y Fp(\()p Fo(E)6 b Fp(\))31 b(where)i Fo(\016)i Fp(is)d(giv)m(en)g(as)386 859 y(in)h(\(2.16\))f(w)m(e)h(infer)g(b)m(y)h (in)m(tegrating)e(\(2.17\))g(\(since)i(lim)2476 874 y Fm(t)p Fn(!1)2663 859 y Fo(t)2708 810 y Fm(@)2745 818 y Ff(\026)2787 810 y Fm(h)p 2708 836 120 4 v 2727 893 a(x)2767 901 y Ff(n)2865 859 y Fp(=)28 b(1)k(\))g(that)984 1073 y(\000)c(=)f Fo(\015)1227 1088 y Fj(1)1289 1073 y Fp(+)22 b Fo(O)1465 993 y Fi(\000)1510 1073 y Fk(j)p Fo(\015)5 b Fk(j)1622 1032 y Fj(2)1660 993 y Fi(\001)1734 1073 y Fp(=)27 b Fo(O)1915 963 y Fi(\020)1974 1073 y Fo(t)2009 1032 y Fm(\014)2052 1009 y Ff(s)2049 1053 y Fh(1)2086 1032 y Fj(\()p Fm(E)t Fj(\)+)p Fm(\017)2280 1009 y Fc(0)2306 963 y Fi(\021)2365 1073 y Fp(;)115 b Fo(\017)2546 1032 y Fn(0)2597 1073 y Fo(>)27 b Fp(0)p Fo(:)349 b Fp(\(2.23\))386 1278 y Fg(R)-5 b(emark)57 b Fp(2.3)p Fg(.)48 b Fp(W)-8 b(e)46 b(could)g(ha)m(v)m(e)h(used)g(a)e (di\013eren)m(t)i(observ)-5 b(able)47 b(constructed)386 1395 y(b)m(y)e(a)e(similar)i(iteration)f(using)h(as)f Fo(\015)1818 1358 y Fj(\(1\))1956 1395 y Fp(a)f(comp)s(onen)m(t)i(of)f Fo(\015)49 b Fp(corresp)s(onding)386 1511 y(to)c(an)h(eigen)m(v)m (ector)i(with)e(eigen)m(v)-5 b(alue)48 b Fo(\025)p Fp(\()p Fo(E)6 b Fp(\))45 b(ha)m(ving)i(Re)17 b(\()o Fo(\025)p Fp(\()p Fo(E)6 b Fp(\)\))50 b Fo(>)g Fp(0.)83 b(W)-8 b(e)386 1627 y(w)m(ould)38 b(again)e(need)i(smo)s(othness)g(of)f(the)g (eigen)m(v)m(ector)i(and)e(a)g(non-resonance)386 1743 y(condition)30 b(for)f Fo(\025)p Fp(\()o Fo(E)1123 1758 y Fj(0)1163 1743 y Fp(\),)h(cf.)43 b(\(H7\))29 b(and)g(\(H8\).)42 b(The)31 b(analogous)e(observ)-5 b(able)30 b Fo(\015)3253 1707 y Fj(\()q Fm(m)p Fj(\))386 1862 y Fp(decreases)i(as)d Fo(t)958 1826 y Fn(\000)p Fm(\016)r Fj(\()r Fm(m)p Fj(+1\))1288 1862 y Fp(with)h(no)g(upp)s(er)g(b)s(ound)g(on)f Fo(m)h Fp(\(assuming)g Fo(E)2991 1877 y Fj(0)3061 1862 y Fp(is)g(not)f(a)386 1979 y(resonance)34 b(of)e(an)m(y)h(order\).)44 b(But)32 b(as)h(w)m(e)g(will)h(see)f(b)s(elo)m(w,)h(the)f(corresp)s(ondence)386 2095 y(b)s(et)m(w)m(een)41 b(classical)f(and)f(quan)m(tum)h(b)s(eha)m (vior)f(is)g(not)g(so)g(precise)h(as)f(to)f(allo)m(w)386 2211 y(a)j(similar)i(statemen)m(t)g(in)f(Quan)m(tum)g(Mec)m(hanics.)73 b(Th)m(us)43 b(it)f(do)s(es)g(not)f(m)m(uc)m(h)386 2327 y(matter)33 b(whic)m(h)h(of)e(these)i(observ)-5 b(ables)34 b(is)f(used.)386 2506 y(2.3.)48 b FC(Quan)m(tum)56 b Fp(\000)p FC(.)49 b Fp(T)-8 b(o)47 b(get)g(a)g(statemen)m(t)i(lik)m(e)g (\(2.23\))d(in)i(Quan)m(tum)f(Me-)386 2626 y(c)m(hanics)31 b(w)m(e)g(need)g(to)f(quan)m(tize)h(the)g(classical)g(sym)m(b)s(ol)g Fo(\015)2517 2589 y Fj(\()q Fm(m)p Fj(\))2666 2626 y Fp(=)d Fo(\015)2826 2589 y Fj(\()p Fm(m)p Fj(\))2947 2626 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\).)42 b(W)-8 b(e)386 2742 y(c)m(ho)s(ose)27 b(a)f(quan)m(tization)h(that)f(tak)m(es)h(in)m (to)f(accoun)m(t)h(lo)s(calizations)g(of)e(the)i(states)386 2858 y Fo( )34 b Fp(=)29 b Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )38 b Fp(ob)s(eying)e(\(1.8\))d(and)h(\(1.9\))o(.)47 b(W)-8 b(e)35 b(\014x)f Fo(m)c Fp(=)g Fo(m)2592 2873 y Fj(0)2665 2858 y Fp(dep)s(ending)35 b(on)f(an)386 2974 y(analogue)h(of)g(the)h(classical)g(b)s(ound)g(\(2.16\),)f(cf.)52 b(the)36 b(classical)h(case)f(discussed)386 3091 y(ab)s(o)m(v)m(e.)68 b(Without)41 b(going)f(in)m(to)g(details,)k(in)c(the)h(case)g(of)f (\(2.8\))g(this)h(op)s(erator)386 3207 y(tak)m(es)34 b(the)f(form)651 3372 y(\000)27 b(=)h(\000\()p Fo(t)p Fp(\))g(=)f(\()p Fo(p)22 b Fk(\000)h Fo(\030)5 b Fp(\()o Fo(E)1512 3387 y Fj(0)1552 3372 y Fp(\)\))22 b Fk(\001)g Fo(!)1761 3387 y Fm(l)1786 3372 y Fp(\()p Fo(E)1896 3387 y Fj(0)1936 3372 y Fp(\))g(+)g Fo(B)2168 3387 y Fj(1)2208 3372 y Fp(\()o Fo(t)p Fp(\))q(;)114 b Fo(B)2534 3387 y Fj(1)2573 3372 y Fp(\()p Fo(t)p Fp(\))33 b(b)s(ounded)q Fo(:)386 3537 y Fp(Strictly)g(sp)s(eaking)h(to)e(get)h(this)g (expression)i(w)m(e)f(\014rst)f(mak)m(e)g(the)g(mo)s(di\014cation)386 3653 y(of)e(the)h(classical)i(\000)d(of)h(dividing)h(b)m(y)f(the)h (constan)m(t)f Fo(c)2353 3668 y Fm(l)2407 3653 y Fp(=)c Fo(@)2562 3668 y Fm(\021)2597 3680 y Ff(l)2626 3653 y Fo(\015)2677 3668 y Fj(1)2716 3653 y Fp(\()p Fo(w)s(;)17 b(E)2943 3668 y Fj(0)2982 3653 y Fp(\))3019 3682 y Fn(j)p Fm(w)r Fj(=0)3218 3653 y Fp(and)386 3782 y(then)39 b(taking)f(the)g (real)g(part;)j(w)m(e)e(shall)f(not)g(discuss)i(the)f(case)g(of)e (\(2.9\))h(here.)386 3898 y(W)-8 b(e)33 b(sho)m(w)h(the)f(follo)m(wing) f(analogue)h(of)f(\(2.23\):)486 4015 y(Giv)m(en)h Fo(\033)e(>)d Fp(0)k(w)m(e)h(ha)m(v)m(e)h(for)e(some)h(\000)f(of)g(this)h(form)f(the) g(strong)h(lo)s(calization)1068 4095 y Fi(\015)1068 4155 y(\015)1123 4180 y Fp(1)1172 4196 y Fj([)p Fm(t)1217 4178 y Ff(\033)r Fc(\000)p Fh(1)1337 4196 y Fm(;)p Fn(1)p Fj(\))1459 4180 y Fp(\()p Fk(j)p Fp(\000)p Fk(j)p Fp(\))o Fo(e)1696 4139 y Fn(\000)p Fm(itH)1868 4180 y Fo( )1935 4095 y Fi(\015)1935 4155 y(\015)2018 4180 y Fk(!)27 b Fp(0)33 b(for)f Fo(t)c Fk(!)f(1)p Fo(:)432 b Fp(\(2.24\))486 4347 y(W)-8 b(e)32 b(notice)g(that)f(\(2.24\))g(is)h(a)g(w)m(eak)m(er)h (b)s(ound)f(than)g(\(2.23\);)f(to)g(con)m(trol)h(v)-5 b(ar-)386 4463 y(ious)40 b(comm)m(utators)h(w)m(e)f(need)h(to)e(ha)m(v) m(e)i Fo(\033)j Fp(p)s(ositiv)m(e.)66 b(On)40 b(the)g(other)g(hand)g (it)386 4579 y(ma)m(y)f(app)s(ear)f(somewhat)h(surprising)g(that)f(suc) m(h)h(lo)s(calization)f(result)h(can)f(b)s(e)386 4695 y(pro)m(v)m(ed)f(at)f(all)g(for)f Fo(\033)j(<)33 b Fp(2)1371 4659 y Fn(\000)p Fj(1)1465 4695 y Fp(.)54 b(According)36 b(to)g(folklore)g(wisdom)h(there)g(is)f(usu-)386 4812 y(ally)k(a)g(strong)g(connection)h(for)e(pseudo)s(di\013eren)m(tial)j (op)s(erators)d(b)s(et)m(w)m(een)j(the)386 4928 y(functional)29 b(calculus)h(and)e(the)h(pseudo)s(di\013eren)m(tial)i(calculus,)g(see)e (for)f(example)386 5044 y([DG,)c(App)s(endix)i(D].)e(In)h(our)f(case)h (one)g(migh)m(t)g(think)h(that)e(\(2.24\))g(is)h(equiv)-5 b(alen)m(t)386 5160 y(to)32 b(a)g(statemen)m(t)j(lik)m(e)1115 5325 y Fo(e)1160 5284 y Fn(\000)p Fm(itH)1332 5325 y Fo( )c Fk(\031)e Fo(a)1583 5284 y Fm(w)1583 5350 y(t)1639 5325 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(e)1908 5284 y Fn(\000)p Fm(itH)2080 5325 y Fo( )37 b Fp(for)32 b Fo(t)c Fk(!)f(1)p Fo(;)386 5494 y Fp(where)38 b(the)f(sym)m(b)s(ol)h Fo(a)1233 5509 y Fm(t)1297 5494 y Fp(=)c Fo(h)1463 5413 y Fi(\000)1509 5494 y Fo(t)1544 5457 y Fj(1)p Fn(\000)p Fm(\033)1698 5494 y Fp(Re)1830 5413 y Fi(\000)1875 5494 y Fo(c)1917 5452 y Fn(\000)p Fj(1)1917 5521 y Fm(l)2012 5494 y Fo(\015)2068 5457 y Fj(\()p Fm(m)2157 5466 y Fh(0)2192 5457 y Fj(\))2224 5413 y Fi(\001)o(\001)2351 5494 y Fp(for)i(suitable)i Fo(h)d Fk(2)g Fo(C)3141 5457 y Fn(1)3134 5518 y Fj(0)3215 5494 y Fp(\()p FC(R)p Fp(\))386 5623 y(and)d Fo(\015)631 5587 y Fj(\()p Fm(m)720 5596 y Fh(0)755 5587 y Fj(\))818 5623 y Fp(giv)m(en)h(b)m(y)g(the)f(classical)h(sym)m(b)s(ol)g(\(p)s (ossibly)g(mo)s(di\014ed)f(b)m(y)h(cut-o\013s\))p eop end %%Page: 15 15 TeXDict begin 15 14 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(15)386 459 y Fp(discussed)38 b(ab)s(o)m(v)m(e.)51 b(Ho)m(w)m(ev)m(er)37 b(for)d Fo(\033)i(<)31 b Fp(2)1927 423 y Fn(\000)p Fj(1)2056 459 y Fp(suc)m(h)37 b(sym)m(b)s(ols)f Fo(a)2704 474 y Fm(t)2769 459 y Fp(do)f(not)f(\014t)h(in)m(to)386 575 y(an)m(y)30 b(standard)g(\(parameter-dep)s(enden)m(t\))h(pseudo)s (di\013eren)m(tial)h(calculus)f(whic)m(h)386 702 y(essen)m(tially)41 b(w)m(ould)e(require)g(the)g(uniform)f(b)s(ounds)h Fo(@)2428 654 y Fm(\014)2423 729 y(\030)2476 702 y Fo(@)2532 665 y Fm(\013)2527 726 y(x)2582 702 y Fo(a)2633 717 y Fm(t)2700 702 y Fp(=)e Fo(O)2891 621 y Fi(\000)2936 702 y Fo(t)2971 665 y Fm(\016)3002 674 y Fh(2)3037 665 y Fn(j)p Fm(\014)s Fn(j\000)p Fm(\016)3206 674 y Fh(1)3240 665 y Fn(j)p Fm(\013)p Fn(j)3329 621 y Fi(\001)386 825 y Fp(with)i Fo(\016)657 840 y Fj(2)736 825 y Fo(<)f(\016)893 840 y Fj(1)933 825 y Fp(.)62 b(As)40 b(a)e(consequence)k(w)m(e)e(shall)g (base)f(our)g(pro)s(of)f(of)h(\(2.24\))f(on)386 941 y(a)45 b(functional)g(calculus)h(approac)m(h.)82 b(Using)45 b(a)g(di\013eren)m(tial)h Fg(e)-5 b(quality)54 b Fp(related)386 1058 y(to)42 b(\(2.17\))g(w)m(e)i(can)e(indeed)i(b)s(ound)f(certain)g (quan)m(tum)h(errors)f(in)g(a)f(calculus)386 1174 y(ev)m(en)f(for)f Fo(\033)k(<)c Fp(2)1036 1138 y Fn(\000)p Fj(1)1130 1174 y Fp(.)65 b(It)40 b(is)g(imp)s(ortan)m(t)g(that)g(w)m(e)h(can)f(tak)m (e)g Fo(\033)k Fp(small;)g(see)d(the)386 1290 y(next)33 b(subsection.)45 b(Somewhat)33 b(related)f(problems)i(w)m(ere)f (studied)g(in)f([G1])g(and)386 1406 y([CHS1].)386 1582 y Fg(R)-5 b(emark.)43 b Fp(Although)c(suppressed)h(in)e(the)h(ab)s(o)m (v)m(e)f(discussion)j(it)d(is)g Fg(imp)-5 b(ortant)386 1699 y Fp(from)21 b(a)h(calculus)h(p)s(oin)m(t)f(of)f(view)j(that)d (the)h(lo)s(calization)g(similar)h(to)e(the)h(classical)386 1815 y(b)s(ound)33 b(\(2.16\))f(used)i(to)e(de\014ne)i(\000)f(and)g (pro)m(ving)g(\(2.24\))f(is)i(\\somewhat)g(w)m(eak")386 1931 y(\(to)g(b)s(e)h(sp)s(eci\014ed)h(later\);)g(in)f(particular)g(it) f(m)m(ust)i(b)s(e)f(w)m(eak)m(er)h(than)f(that)f(used)386 2047 y(\(and)f(b)s(eing)g(of)f(the)h(same)h(t)m(yp)s(e\))f(in)g(the)h (uncertain)m(t)m(y)g(principle)h(argumen)m(t)e(of)386 2164 y(the)g(next)g(subsection,)i(see)f(\(2.25\).)386 2339 y(2.4.)48 b FC(Implemen)m(ting)58 b(the)d(uncertain)m(t)m(y)i (principle.)49 b Fp(The)h(last)f(step)g(in)386 2456 y(our)29 b(pro)s(of)f(of)h(Theorem)h(1.1)f(is)h(the)f(decisiv)m(e)j(one;)f(here) e(Quan)m(tum)h(Mec)m(hanics)386 2572 y(en)m(ters)43 b(crucially)-8 b(.)73 b(W)-8 b(e)42 b(sho)m(w)h(that)f(a)f(lo)s(calization)h(similar)g (to)g(the)g(classical)386 2688 y(b)s(ound)31 b(\(2.16\))f(and)h (\(2.24\))f(are)h(incompatible)h(unless)h Fo( )e Fp(=)d(0.)42 b(First)31 b(\014x)h Fo(\016)f(>)d Fp(0)386 2804 y(in)33 b(agreemen)m(t)h(with)f(\(2.16\).)42 b(More)33 b(precisely)i(w)m(e)f (need)g(the)f(lo)s(calization)1049 2968 y Fo(e)1094 2927 y Fn(\000)p Fm(itH)1266 2968 y Fo( )e Fk(\031)e Fo(h)1522 2983 y Fj(2)1561 2887 y Fi(\000)1633 2943 y Fp(\026)1607 2968 y Fo(A)1680 2887 y Fi(\001)1726 2968 y Fo(e)1771 2927 y Fn(\000)p Fm(itH)1942 2968 y Fo( )j Fk(!)27 b Fp(0)33 b(for)f Fo(t)c Fk(!)f(1)p Fo(;)413 b Fp(\(2.25\))386 3129 y(for)32 b(some)h Fo(h)835 3144 y Fj(2)903 3129 y Fk(2)28 b Fo(C)1074 3093 y Fn(1)1067 3154 y Fj(0)1148 3129 y Fp(\()p FC(R)p Fp(\))k(and)h(some)g(op)s(erator)f(of)g(the)h (form)748 3268 y(\026)723 3293 y Fo(A)27 b Fp(=)h Fo(t)962 3252 y Fm(\016)r Fn(\000)p Fj(1)1090 3293 y Fo(x)1145 3308 y Fm(l)1194 3293 y Fp(+)22 b Fo(B)1366 3308 y Fj(2)1405 3293 y Fp(\()p Fo(t)p Fp(\))q(;)114 b Fo(B)1732 3308 y Fj(2)1771 3293 y Fp(\()p Fo(t)p Fp(\))28 b(=)g Fo(O)2092 3213 y Fi(\000)2137 3293 y Fo(t)2172 3252 y Fm(\016)2210 3213 y Fi(\001)2255 3293 y Fo(;)115 b(x)2452 3308 y Fm(l)2506 3293 y Fp(=)27 b Fo(x)c Fk(\001)f Fo(!)2798 3308 y Fm(l)2823 3293 y Fp(\()p Fo(E)2933 3308 y Fj(0)2973 3293 y Fp(\))p Fo(:)386 3455 y Fp(Then)34 b(\014x)f(an)m(y)g Fo(\033)f Fk(2)c Fp(\(0)p Fo(;)17 b(\016)t Fp(\))32 b(and)h(in)m(tro)s(duce)g (with)g(\000)g(as)g(in)f(\(2.24\))g(the)h(op)s(erator)411 3546 y(\026)386 3571 y Fo(H)i Fp(=)28 b Fo(t)641 3535 y Fj(1)p Fn(\000)p Fm(\016)769 3571 y Fp(\000.)486 3687 y(W)-8 b(e)33 b(pro)m(v)m(e)g(a)g(global)f(Mourre)h(estimate)1543 3847 y Fo(i)1576 3766 y Fi(\002)1643 3822 y Fp(\026)1617 3847 y Fo(H)8 b(;)1775 3822 y Fp(\026)1750 3847 y Fo(A)1823 3766 y Fi(\003)1892 3847 y Fk(\025)28 b Fp(2)2046 3806 y Fn(\000)p Fj(1)2140 3847 y Fo(I)8 b(:)907 b Fp(\(2.26\))486 4008 y(Abstract)33 b(Mourre)g(theory)g(and)g(\(2.26\))f(lead)h(to)f (the)h(b)s(ound)1205 4091 y Fi(\015)1205 4151 y(\015)1261 4176 y Fo(h)1317 4191 y Fj(2)1356 4095 y Fi(\000)1428 4151 y Fp(\026)1402 4176 y Fo(A)1475 4095 y Fi(\001)1521 4176 y Fo(h)1577 4191 y Fj(1)1616 4095 y Fi(\000)1662 4176 y Fo(t)1697 4135 y Fm(\016)r Fn(\000)p Fm(\033)1858 4151 y Fp(\026)1833 4176 y Fo(H)1921 4095 y Fi(\001)1967 4091 y(\015)1967 4151 y(\015)2050 4176 y Fk(\024)28 b Fo(C)7 b(t)2267 4135 y Fj(\()q Fm(\033)r Fn(\000)p Fm(\016)r Fj(\))q Fm(=)p Fj(2)2528 4176 y Fo(;)570 b Fp(\(2.27\))386 4338 y(v)-5 b(alid)33 b(for)f(all)g Fo(h)962 4353 y Fj(1)1002 4338 y Fo(;)17 b(h)1102 4353 y Fj(2)1169 4338 y Fk(2)28 b Fo(C)1340 4301 y Fn(1)1333 4362 y Fj(0)1414 4338 y Fp(\()p FC(R)p Fp(\).)486 4454 y(Finally)37 b(pic)m(king)i(lo)s (calization)f(functions)g(in)g(agreemen)m(t)h(with)f(\(2.25\))f(and)386 4570 y(\(2.24\))32 b(w)m(e)h(conclude)h(from)f(\(2.27\))f(that)826 4734 y Fo(e)871 4693 y Fn(\000)p Fm(itH)1043 4734 y Fo( )f Fk(\031)e Fo(h)1299 4749 y Fj(2)1338 4653 y Fi(\000)1410 4709 y Fp(\026)1384 4734 y Fo(A)1457 4653 y Fi(\001)1503 4734 y Fo(h)1559 4749 y Fj(1)1598 4653 y Fi(\000)1644 4734 y Fo(t)1679 4693 y Fm(\016)r Fn(\000)p Fm(\033)1840 4709 y Fp(\026)1815 4734 y Fo(H)1903 4653 y Fi(\001)1949 4734 y Fo(e)1994 4693 y Fn(\000)p Fm(itH)2166 4734 y Fo( )i Fk(!)d Fp(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(;)386 4894 y Fp(completing)34 b(the)f(pro)s(of.)1474 5100 y(3.)48 b Fq(Preliminaries)486 5274 y Fp(W)-8 b(e)22 b(use)i(the)f(notation)f (\011\()p Fo(m;)17 b(g)t Fp(\))22 b(for)g(the)g(space)i(of)e(op)s (erators)g(giv)m(en)i(b)m(y)g(quan-)386 5390 y(tizing)30 b(sym)m(b)s(ols)h(in)f(the)g(sym)m(b)s(ol)h(class)g Fo(S)6 b Fp(\()p Fo(m;)17 b(g)t Fp(\))29 b(as)g(de\014ned)j(b)m(y)e([H\177)-49 b(o,)30 b(\(18.4.6\)].)386 5506 y(F)-8 b(or)25 b(the)i(w)m(eigh)m(t)h (functions)f Fo(m)f Fp(and)h(metrics)g Fo(g)j Fp(relev)-5 b(an)m(t)27 b(for)f(this)h(pap)s(er)f(it)g(do)s(es)386 5623 y(not)31 b(matter)h(here)g(whether)g(\\quan)m(tize")h(refers)f(to) f(W)-8 b(eyl)32 b(or)f(Kohn-Niren)m(b)s(erg)p eop end %%Page: 16 16 TeXDict begin 16 15 bop 386 259 a Fl(16)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y Fp(quan)m(tization.)55 b(F)-8 b(or)35 b Fo(a)f Fk(2)g Fo(S)6 b Fp(\()p Fo(m;)17 b(g)t Fp(\))35 b(w)m(e)i(use)g(the)g(notation)e Fo(a)2653 423 y Fm(w)2710 459 y Fp(\()p Fo(x;)17 b(p)p Fp(\))36 b(to)g(denote)386 575 y(the)e(W)-8 b(eyl)34 b(quan)m(tization)h(of)e Fo(a)p Fp(.)46 b(W)-8 b(e)34 b(refer)g(the)g(reader)g(to)f([DG,)g(App)s (endix)i(D])386 691 y(and)e([H\177)-49 b(o,)34 b(Chapter)g(18])f(for)g (a)g(detailed)h(accoun)m(t)h(of)d(the)i(calculus)h(of)e(pseudo-)386 807 y(di\013eren)m(tial)k(op)s(erators.)54 b(W)-8 b(e)36 b(shall)h(deal)g(with)f(v)-5 b(arious)37 b(kinds)g(of)f(parameter-)386 924 y(dep)s(enden)m(t)k(sym)m(b)s(ols.)62 b(In)38 b(one)g(case)h(the)g (parameter)f(is)h(time)g Fo(t)e Fk(\025)g Fp(1)h(and)g(for)386 1040 y(that)32 b(w)m(e)i(in)m(tro)s(duce)f(the)g(follo)m(wing)g (shorthand)h(notation.)386 1221 y FC(De\014nition)44 b(3.1.)g Fg(A)c(family)f Fk(f)p Fo(a)1647 1236 y Fm(t)1677 1221 y Fk(j)p Fo(t)27 b Fk(\025)h Fp(1)p Fk(g)39 b Fg(of)g(symb)-5 b(ols)39 b(in)g Fo(S)6 b Fp(\()p Fo(m;)17 b(g)t Fp(\))39 b Fg(is)g(said)g(to)386 1337 y(b)-5 b(e)33 b(uniform)g(in)g Fo(S)6 b Fp(\()o Fo(m;)17 b(g)t Fp(\))33 b Fg(if)g(for)g(al)5 b(l)33 b(semi-norms)f Fk(jj)18 b(\001)g(jj)2436 1352 y Fm(k)2512 1337 y Fg(on)33 b Fo(S)6 b Fp(\()o Fo(m;)17 b(g)t Fp(\))33 b Fg(\(cf.)44 b([H\177)-50 b(o,)386 1453 y(\(18.4.6\)]\))36 b Fp(sup)979 1477 y Fm(t)1025 1453 y Fk(k)p Fo(a)1126 1468 y Fm(t)1156 1453 y Fk(k)1206 1468 y Fm(k)1281 1453 y Fo(<)d Fk(1)p Fg(.)52 b(In)37 b(this)h(c)-5 b(ase)37 b(we)g(write)h Fo(a)2553 1468 y Fm(t)2615 1453 y Fk(2)33 b Fo(S)2774 1468 y Fm(unif)2927 1453 y Fp(\()p Fo(m;)17 b(g)t Fp(\))37 b Fg(and)386 1570 y Fo(a)437 1533 y Fm(w)437 1594 y(t)494 1570 y Fp(\()p Fo(x;)17 b(p)p Fp(\))27 b Fk(2)h Fp(\011)915 1585 y Fm(unif)1068 1570 y Fp(\()p Fo(m;)17 b(g)t Fp(\))p Fg(.)486 1750 y Fp(Giv)m(en)35 b(this)h(uniformit)m(y)f(prop)s(ert)m(y)h(v)-5 b(arious)35 b(b)s(ounds)g(from)g(the)g(calculus)h(of)386 1867 y(pseudo)s(di\013eren)m(tial)c(op)s(erators)d(are)h(uniform)g(in)g (the)g(parameter)g(\(b)m(y)h(con)m(tin)m(u-)386 1983 y(it)m(y)i(prop)s(erties)h(of)e(the)h(calculus\).)486 2099 y(W)-8 b(e)41 b(shall)g(also)g(deal)h(with)f(parameter-dep)s (enden)m(t)i(metrics.)70 b(Sp)s(eci\014cally)386 2215 y(w)m(e)34 b(shall)f(consider)h(for)e(0)27 b Fk(\024)h Fo(\016)1511 2230 y Fj(2)1579 2215 y Fo(<)f(\016)1725 2230 y Fj(1)1792 2215 y Fk(\024)i Fp(1)j(and)h Fo(t)27 b Fk(\025)i Fp(1)1225 2384 y Fo(g)1272 2399 y Fm(t)1329 2384 y Fp(=)f Fo(g)1484 2337 y Fm(\016)1515 2346 y Fh(1)1549 2337 y Fm(;\016)1600 2346 y Fh(2)1480 2407 y Fm(t)1666 2384 y Fp(=)f Fo(t)1804 2343 y Fn(\000)p Fj(2)p Fm(\016)1925 2352 y Fh(1)1965 2384 y Fo(dx)2071 2343 y Fj(2)2133 2384 y Fp(+)22 b Fo(t)2266 2343 y Fj(2)p Fm(\016)2332 2352 y Fh(2)2371 2384 y Fo(d\030)2470 2343 y Fj(2)2509 2384 y Fo(:)638 b Fp(\(3.1\))386 2553 y(Similarly)51 b(to)f(De\014nition)h (3.1)f(w)m(e)h(shall)g(write)g(\(for)f(giv)m(en)h Fo(l)60 b Fk(2)e FC(R)p Fp(\),)d Fo(a)3221 2568 y Fm(t)3308 2553 y Fk(2)386 2671 y Fo(S)446 2686 y Fm(unif)599 2590 y Fi(\000)645 2671 y Fo(t)680 2635 y Fm(l)706 2671 y Fo(;)17 b(g)797 2686 y Fm(t)826 2590 y Fi(\001)918 2671 y Fp(and)47 b Fo(a)1173 2635 y Fm(w)1173 2695 y(t)1230 2671 y Fp(\()p Fo(x;)17 b(p)p Fp(\))52 b Fk(2)g Fp(\011)1700 2686 y Fm(unif)1853 2590 y Fi(\000)1898 2671 y Fo(t)1933 2635 y Fm(l)1960 2671 y Fo(;)17 b(g)2051 2686 y Fm(t)2080 2590 y Fi(\001)2172 2671 y Fp(meaning)47 b(that)g(for)f(all)h(\(time-) 386 2789 y(dep)s(enden)m(t\))h(semi-norms)g(sup)1585 2812 y Fm(t)1632 2789 y Fk(k)p Fo(a)1733 2804 y Fm(t)1762 2789 y Fk(k)1812 2804 y Fm(t;k)1951 2789 y Fo(<)i Fk(1)p Fp(.)84 b(Also)47 b(in)f(this)h(case)g(v)-5 b(arious)386 2905 y(b)s(ounds)23 b(from)f(the)g(calculus)i(of)d(pseudo)s(di\013eren) m(tial)j(op)s(erators)e(will)h(b)s(e)f(uniform)386 3021 y(in)40 b(the)g(parameter.)66 b(Some)41 b(extensions)h(of)e(this)g (idea)g(will)h(b)s(e)f(used)h(without)386 3137 y(further)33 b(commen)m(ts.)486 3253 y(One)27 b(ma)m(y)g(v)m(erify)h(that)f (\(1.10\))e(follo)m(ws)j(from)e(\(1.8\))g(b)m(y)i(applying)f(a)g (partition)386 3370 y(of)35 b(unit)m(y)h(to)e(the)i Fo(f)46 b Fp(of)34 b(an)m(y)i(state)f Fo( )h Fp(=)c Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )39 b Fp(of)j(\(1.8\))34 b(to)h(decomp)s (ose)h(it)f(as)386 3486 y Fo(f)63 b Fp(=)624 3411 y Fi(P)746 3486 y Fo(f)794 3501 y Fm(i)869 3486 y Fp(and)47 b(b)m(y)h(noticing)f (that)f(\(1.8\))h(remains)h(v)-5 b(alid)47 b(for)f(the)h(sharp)s(er)386 3602 y(lo)s(calized)36 b(states)f Fo( )h Fk(!)31 b Fo( )1359 3617 y Fm(i)1419 3602 y Fp(=)h Fo(f)1575 3617 y Fm(i)1603 3602 y Fp(\()p Fo(H)8 b Fp(\))o Fo( )t Fp(.)51 b(\(Notice)35 b(that)g(if)g(supp)17 b(\()p Fo(f)2867 3617 y Fm(i)2895 3602 y Fp(\))35 b(is)h(lo)s(cated)386 3718 y(near)k Fo(E)682 3733 y Fm(i)749 3718 y Fp(this)g(leads)h(to)e Fo(t)1359 3682 y Fn(\000)p Fj(1)1453 3718 y Fo(x)h Fk(\031)g Fo(k)s Fp(\()p Fo(E)1829 3733 y Fm(i)1857 3718 y Fp(\))p Fo(!)t Fp(\()p Fo(E)2070 3733 y Fm(i)2098 3718 y Fp(\))f(and)h Fo(p)f Fk(\031)h Fo(\030)5 b Fp(\()o Fo(E)2734 3733 y Fm(i)2763 3718 y Fp(\))39 b(along)g Fo( )3170 3733 y Fm(i)3199 3718 y Fp(\()p Fo(t)p Fp(\).\))386 3835 y(The)31 b(latter)f(follo)m(ws)h(readily)g(up)s(on)g(comm)m(utation)g(and)f (applying)h(Lemma)g(3.2)386 3951 y(stated)24 b(b)s(elo)m(w.)42 b(The)24 b(same)h(argumen)m(t)g(sho)m(ws)g(that)f(indeed)h Fk(H)2695 3966 y Fj(0)2758 3951 y Fp(is)f Fo(H)8 b Fp({reducing.)386 4067 y(\(This)32 b(prop)s(ert)m(y)g(ma)m(y)g(also)g(b)s(e)f(v)m (eri\014ed)i(without)f(app)s(ealing)f(to)g(Lemma)h(3.2.\))486 4190 y(Pic)m(k)j(non-negativ)m(e)f Fo(g)1327 4205 y Fj(1)1366 4190 y Fo(;)20 b Fp(~)-52 b Fo(g)1457 4205 y Fj(1)1496 4190 y Fo(;)1543 4166 y Fp(~)1543 4190 y(~)g Fo(g)1587 4205 y Fj(1)1655 4190 y Fk(2)30 b Fo(C)1828 4153 y Fn(1)1821 4214 y Fj(0)1903 4190 y Fp(\()p FC(R)2025 4153 y Fm(n)2071 4190 y Fp(\))k(suc)m(h)h(that)e Fo(g)2623 4205 y Fj(1)2692 4190 y Fp(=)c(1)k(in)h(a)f(\(small\))386 4306 y(neigh)m(b)s(orho)s(o)s (d)38 b(of)h Fo(k)s Fp(\()p Fo(E)1286 4321 y Fj(0)1325 4306 y Fp(\))p Fo(!)1424 4321 y Fj(0)1463 4306 y Fp(,)44 b(~)-52 b Fo(g)1578 4321 y Fj(1)1655 4306 y Fp(=)38 b(1)g(in)h(a)g (neigh)m(b)s(orho)s(o)s(d)f(of)g(supp)18 b(\()p Fo(g)3102 4321 y Fj(1)3141 4306 y Fp(\))39 b(and)389 4405 y(~)389 4428 y(~)-52 b Fo(g)433 4443 y Fj(1)517 4428 y Fp(=)45 b(1)e(in)g(a)f(neigh)m(b)s(orho)s(o)s(d)h(of)f(supp)18 b(\()s(~)-52 b Fo(g)1992 4443 y Fj(1)2031 4428 y Fp(\).)74 b(Similarly)-8 b(,)47 b(pic)m(k)d(non-negativ)m(e)386 4551 y Fo(g)433 4566 y Fj(2)472 4551 y Fo(;)20 b Fp(~)-52 b Fo(g)563 4566 y Fj(2)602 4551 y Fo(;)649 4528 y Fp(~)649 4551 y(~)g Fo(g)693 4566 y Fj(2)759 4551 y Fk(2)29 b Fo(C)931 4515 y Fn(1)924 4576 y Fj(0)1005 4551 y Fp(\()p FC(R)1127 4515 y Fm(n)1174 4551 y Fp(\))f(suc)m(h)i(that)e Fo(g)1710 4566 y Fj(2)1777 4551 y Fp(=)g(1)g(in)h(a)f(neigh)m(b)s(orho) s(o)s(d)g(of)g Fo(\030)2903 4566 y Fj(0)2942 4551 y Fp(,)33 b(~)-52 b Fo(g)3046 4566 y Fj(2)3113 4551 y Fp(=)27 b(1)h(in)386 4674 y(a)g(neigh)m(b)s(orho)s(o)s(d)g(of)g(supp)18 b(\()p Fo(g)1481 4689 y Fj(2)1520 4674 y Fp(\))28 b(and)1775 4650 y(~)1775 4674 y(~)-52 b Fo(g)1819 4689 y Fj(2)1885 4674 y Fp(=)28 b(1)g(in)h(a)f(neigh)m(b)s(orho)s(o)s(d)g(of)g(supp)18 b(\()s(~)-52 b Fo(g)3271 4689 y Fj(2)3310 4674 y Fp(\).)386 4796 y(W)-8 b(e)28 b(supp)s(ose)h(supp)1129 4715 y Fi(\000)1178 4773 y Fp(~)1178 4796 y(~)-53 b Fo(g)1221 4811 y Fj(1)1260 4715 y Fi(\001)1318 4796 y Fk(\002)12 b Fp(supp)1626 4715 y Fi(\000)1675 4773 y Fp(~)1675 4796 y(~)-53 b Fo(g)1718 4811 y Fj(2)1757 4715 y Fi(\001)1831 4796 y Fk(\022)28 b(U)1998 4811 y Fj(0)2065 4796 y Fp(\(with)g Fk(U)2382 4811 y Fj(0)2450 4796 y Fp(giv)m(en)h(as)e(in)h(\(1.9\)\),)h(and)386 4912 y(in)k(fact)f(that)g(the)h(supp)s(orts)h(are)e(so)h(small)g(that)g (for)f(some)h Fo(t)2648 4927 y Fj(0)2716 4912 y Fk(\025)28 b Fp(1)k(the)h(sym)m(b)s(ol)961 5077 y Fo(h)1017 5092 y Fm(t)1047 5077 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\))28 b(:)f(=)h Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))s(~)-52 b Fo(g)1781 5092 y Fj(1)1820 4996 y Fi(\000)1865 5077 y Fo(t)1900 5036 y Fn(\000)p Fj(1)1995 5077 y Fo(x)2050 4996 y Fi(\001)2099 5077 y Fp(~)g Fo(g)2143 5092 y Fj(2)2182 5077 y Fp(\()p Fo(\030)5 b Fp(\))1351 5238 y(=)28 b Fo(h)p Fp(\()p Fo(r)1593 5253 y Fj(0)1638 5238 y Fp(^)-55 b Fo(x)q(;)17 b(\030)5 b Fp(\))r(~)-52 b Fo(g)1864 5253 y Fj(1)1903 5157 y Fi(\000)1949 5238 y Fo(t)1984 5197 y Fn(\000)p Fj(1)2078 5238 y Fo(x)2133 5157 y Fi(\001)2183 5238 y Fp(~)f Fo(g)2226 5253 y Fj(2)2266 5238 y Fp(\()o Fo(\030)5 b Fp(\);)114 b Fo(t)28 b Fk(\025)g Fo(t)2733 5253 y Fj(0)2773 5238 y Fo(;)3174 5159 y Fp(\(3.2\))386 5412 y(cf.)44 b(\(H1\).)f(By)33 b(the)g(assumption)h(\(H2\))e(w)m(e)i (then)f(ha)m(v)m(e)1203 5588 y Fo(h)1259 5603 y Fm(t)1317 5588 y Fk(2)28 b Fo(S)1471 5603 y Fm(unif)1624 5588 y Fp(\(1)p Fo(;)17 b(g)1802 5603 y Fj(0)1840 5588 y Fp(\))22 b Fk(\\)h Fo(S)2049 5603 y Fm(unif)2202 5507 y Fi(\000)2248 5588 y Fp(1)p Fo(;)17 b(g)2392 5541 y Fj(1)p Fm(;)p Fj(0)2388 5610 y Fm(t)2485 5507 y Fi(\001)2530 5588 y Fo(:)617 b Fp(\(3.3\))p eop end %%Page: 17 17 TeXDict begin 17 16 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(17)386 459 y FC(Lemma)39 b(3.2.)j Fg(F)-7 b(or)34 b(al)5 b(l)34 b Fo(f)39 b Fk(2)28 b Fo(C)1578 423 y Fn(1)1571 483 y Fj(0)1652 459 y Fp(\()p FC(R)p Fp(\))35 b Fg(the)g(family)1008 636 y Fo(f)11 b Fp(\()p Fo(h)1161 594 y Fm(w)1161 660 y(t)1217 636 y Fp(\()p Fo(x;)17 b(p)p Fp(\)\))28 b Fk(2)g Fp(\011)1677 651 y Fm(unif)1830 636 y Fp(\(1)p Fo(;)17 b(g)2008 651 y Fj(0)2047 636 y Fp(\))22 b Fk(\\)g Fp(\011)2271 651 y Fm(unif)2424 555 y Fi(\000)2470 636 y Fp(1)p Fo(;)17 b(g)2614 588 y Fj(1)p Fm(;)p Fj(0)2610 658 y Fm(t)2707 555 y Fi(\001)3174 636 y Fp(\(3.4\))386 805 y Fg(and)834 850 y Fi(\015)834 910 y(\015)890 934 y Fo(g)937 949 y Fj(1)976 854 y Fi(\000)1022 934 y Fo(t)1057 893 y Fn(\000)p Fj(1)1151 934 y Fo(x)1206 854 y Fi(\001)1252 934 y Fo(g)1299 949 y Fj(2)1338 934 y Fp(\()p Fo(p)p Fp(\))p Fk(f)p Fo(f)11 b Fp(\()p Fo(h)1666 893 y Fm(w)1666 959 y(t)1722 934 y Fp(\()p Fo(x;)17 b(p)p Fp(\)\))23 b Fk(\000)f Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fk(g)2379 850 y Fi(\015)2379 910 y(\015)2462 934 y Fp(=)28 b Fo(O)2644 854 y Fi(\000)2689 934 y Fo(t)2724 893 y Fn(\0001)2853 854 y Fi(\001)2899 934 y Fo(:)248 b Fp(\(3.5\))386 1118 y Fg(Pr)-5 b(o)g(of.)41 b Fp(As)i(for)e(\(3.4\))h(w)m(e)h(ma)m(y)g (pro)s(ceed)g(as)f(in)g(the)h(pro)s(ofs)f(of)f([DG,)g(Prop)s(o-)386 1234 y(sitions)g(D.4.7)d(and)i(D.11.2].)64 b(\(One)40 b(v)m(eri\014es)i(the)e(Beals)h(criterion)f(using)g(the)386 1350 y(represen)m(tation)28 b(\(3.10\))d(giv)m(en)j(b)s(elo)m(w)f(and)f (the)h(calculus)h(of)e(pseudo)s(di\013eren)m(tial)386 1466 y(op)s(erators.\))486 1583 y(F)-8 b(or)27 b(\(3.5\))h(w)m(e)h(let) g Fo(B)k Fp(=)27 b Fo(h)1427 1547 y Fm(w)1427 1607 y(t)1484 1583 y Fp(\()p Fo(x;)17 b(p)p Fp(\))28 b(and)h Fo(G)e Fp(=)h Fo(h)2186 1547 y Fm(w)2242 1583 y Fp(\()p Fo(x;)17 b(p)p Fp(\))d Fk(\000)f Fo(h)2626 1547 y Fm(w)2626 1607 y(t)2684 1583 y Fp(\()p Fo(x;)k(p)p Fp(\).)42 b(By)28 b(\(3.10\))436 1805 y Fo(f)11 b Fp(\()o Fo(h)588 1764 y Fm(w)588 1830 y(t)645 1805 y Fp(\()p Fo(x;)17 b(p)p Fp(\)\))f Fk(\000)g Fo(f)11 b Fp(\()p Fo(H)d Fp(\))28 b(=)1386 1738 y(1)p 1381 1782 59 4 v 1381 1873 a Fo(\031)1466 1669 y Fi(Z)1522 1895 y Fd(C)1601 1695 y Fi(\020)1673 1779 y Fp(\026)1661 1805 y Fo(@)1739 1779 y Fp(~)1718 1805 y Fo(f)1776 1695 y Fi(\021)1836 1805 y Fp(\()p Fo(z)t Fp(\))q(\()p Fo(B)f Fk(\000)22 b Fo(z)t Fp(\))2288 1757 y Fn(\000)p Fj(1)2382 1805 y Fo(G)p Fp(\()p Fo(H)30 b Fk(\000)23 b Fo(z)t Fp(\))2795 1757 y Fn(\000)p Fj(1)2890 1805 y Fo(dudv)t(:)48 b Fp(\(3.6\))386 2026 y(F)-8 b(or)32 b(an)m(y)h(large)f Fo(m)c Fk(2)g FC(N)33 b Fp(w)m(e)g(ma)m(y)h(decomp)s (ose)469 2228 y(\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))795 2179 y Fn(\000)p Fj(1)890 2228 y Fo(G)k Fp(=)895 2343 y Fm(m)854 2372 y Fi(X)861 2585 y Fm(k)r Fj(=1)1014 2467 y Fo(ad)1116 2426 y Fm(k)1116 2492 y(B)1177 2467 y Fp(\()p Fo(G)p Fp(\)\()p Fo(B)g Fk(\000)c Fo(z)t Fp(\))1656 2419 y Fn(\000)p Fm(k)1776 2467 y Fp(+)f(\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))2200 2419 y Fn(\000)p Fj(1)2295 2467 y Fo(ad)2397 2426 y Fm(m)2397 2492 y(B)2463 2467 y Fp(\()p Fo(G)p Fp(\)\()p Fo(B)k Fk(\000)c Fo(z)t Fp(\))2943 2419 y Fn(\000)p Fm(m)3064 2467 y Fo(;)83 b Fp(\(3.7\))386 2731 y(yielding)34 b(\(b)m(y)f(the)g(calculus\))630 2981 y Fo(g)677 2996 y Fj(1)716 2900 y Fi(\000)761 2981 y Fo(t)796 2940 y Fn(\000)p Fj(1)891 2981 y Fo(x)946 2900 y Fi(\001)992 2981 y Fo(g)1039 2996 y Fj(2)1078 2981 y Fp(\()p Fo(p)p Fp(\)\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))1530 2933 y Fn(\000)p Fj(1)1624 2981 y Fo(G)k Fp(=)1873 2856 y Fm(m)1832 2886 y Fi(X)1840 3099 y Fm(k)r Fj(=1)1993 2981 y Fo(R)2067 2996 y Fm(k)2109 2981 y Fp(\()p Fo(B)h Fk(\000)22 b Fo(z)t Fp(\))2436 2933 y Fn(\000)p Fm(k)1042 3237 y Fp(+)g Fo(g)1187 3252 y Fj(1)1226 3156 y Fi(\000)1272 3237 y Fo(t)1307 3196 y Fn(\000)p Fj(1)1401 3237 y Fo(x)1456 3156 y Fi(\001)1502 3237 y Fo(g)1549 3252 y Fj(2)1589 3237 y Fp(\()o Fo(p)p Fp(\)\()p Fo(B)28 b Fk(\000)22 b Fo(z)t Fp(\))2040 3189 y Fn(\000)p Fj(1)2134 3237 y Fo(ad)2236 3196 y Fm(m)2236 3262 y(B)2303 3237 y Fp(\()p Fo(G)p Fp(\))o(\()p Fo(B)28 b Fk(\000)22 b Fo(z)t Fp(\))2782 3189 y Fn(\000)p Fm(m)2903 3237 y Fp(;)630 3398 y Fo(R)704 3413 y Fm(k)774 3398 y Fp(=)28 b Fo(O)956 3317 y Fi(\000)1001 3398 y Fo(t)1036 3357 y Fn(\0001)1165 3317 y Fi(\001)1211 3398 y Fo(:)3174 3152 y Fp(\(3.8\))386 3614 y(By)22 b(\(H2\),)i Fo(ad)879 3577 y Fm(m)879 3639 y(B)945 3614 y Fp(\()p Fo(G)p Fp(\))k Fk(2)g Fp(\011)1296 3629 y Fm(unif)1449 3503 y Fi(\020)1508 3614 y Fk(h)p Fo(x)p Fk(i)1641 3565 y Fm(l)q Fn(\000)p Fm(m)1785 3614 y Fo(;)17 b(g)1876 3629 y Fj(0)1914 3503 y Fi(\021)1996 3614 y Fp(and)k(therefore)i Fo(ad)2675 3577 y Fm(m)2675 3639 y(B)2741 3614 y Fp(\()p Fo(G)p Fp(\))28 b(=)f Fo(O)3103 3533 y Fi(\000)3148 3614 y Fo(t)3183 3577 y Fm(l)q Fn(\000)p Fm(m)3327 3533 y Fi(\001)3372 3614 y Fp(,)386 3756 y(whence)835 3841 y Fi(\015)835 3901 y(\015)890 3926 y Fo(g)937 3941 y Fj(1)976 3845 y Fi(\000)1022 3926 y Fo(t)1057 3885 y Fn(\000)p Fj(1)1151 3926 y Fo(x)1206 3845 y Fi(\001)1252 3926 y Fo(g)1299 3941 y Fj(2)1338 3926 y Fp(\()p Fo(p)p Fp(\)\()p Fo(B)h Fk(\000)22 b Fo(z)t Fp(\))1790 3877 y Fn(\000)p Fj(1)1884 3926 y Fo(G)1961 3841 y Fi(\015)1961 3901 y(\015)2044 3926 y Fk(\024)28 b Fo(C)7 b(t)2261 3885 y Fm(l)q Fn(\000)p Fm(m)2405 3926 y Fk(j)17 b Fp(Im)f Fo(z)t Fk(j)2659 3885 y Fn(\000)p Fj(\()q Fm(m)p Fj(+1\))3174 3926 y Fp(\(3.9\))386 4115 y(uniformly)33 b(in)g Fo(z)g Fk(2)28 b Fp(supp)1333 4034 y Fi(\000)1400 4088 y Fp(~)1379 4115 y Fo(f)1438 4034 y Fi(\001)1483 4115 y Fp(.)486 4233 y(Clearly)33 b(\(3.5\))f(follo)m(ws)i(from)e(\(3.6\))g(and)h(\(3.9\).)1038 b Fe(\003)386 4414 y Fg(R)-5 b(emark)39 b Fp(3.3)p Fg(.)d Fp(The)28 b(statemen)m(ts)g(of)e(Lemma)h(3.2)f(extend)h(to)f(an)m(y)h (smo)s(oth)g(func-)386 4539 y(tion)49 b Fo(f)60 b Fp(with)981 4500 y Fm(d)1017 4477 y Ff(k)p 960 4516 116 4 v 960 4574 a Fm(d\025)1037 4555 y Ff(k)1086 4539 y Fo(f)11 b Fp(\()o Fo(\025)p Fp(\))56 b(=)g Fo(O)1543 4459 y Fi(\000)1588 4539 y Fo(\025)1645 4503 y Fm(m)p Fn(\000)p Fm(k)1805 4459 y Fi(\001)1900 4539 y Fp(\(for)49 b(\014xed)h Fo(m)57 b Fk(2)g FC(R)p Fp(\);)g(in)49 b(particular)386 4657 y(Lemma)33 b(3.2)f(holds)i(for)e Fo(f)11 b Fp(\()o Fo(\025)p Fp(\))28 b(=)f Fo(\025)p Fp(.)386 4839 y FC(De\014nition)44 b(3.4.)g Fg(L)-5 b(et)40 b Fk(F)1378 4854 y Fj(+)1476 4839 y Fg(denote)f(the)h(lar)-5 b(gest)39 b(set)h(of)f Fo(F)50 b Fp(=)36 b Fo(F)2835 4854 y Fj(+)2931 4839 y Fk(2)h Fo(C)3111 4803 y Fn(1)3185 4839 y Fp(\()p FC(R)p Fp(\))p Fg(,)386 4957 y(such)h(that)g Fp(0)c Fk(\024)g Fo(F)48 b Fk(\024)34 b Fp(1)p Fg(,)k Fo(F)1423 4921 y Fn(0)1480 4957 y Fk(\025)c Fp(0)p Fo(;)17 b(F)1761 4921 y Fn(0)1818 4957 y Fk(2)34 b Fo(C)1995 4921 y Fn(1)1988 4981 y Fj(0)2069 4876 y Fi(\000\000)2171 4918 y Fj(1)p 2171 4934 36 4 v 2171 4991 a(2)2216 4957 y Fo(;)2270 4918 y Fj(3)p 2270 4934 V 2270 4991 a(4)2315 4876 y Fi(\001\001)2406 4957 y Fg(,)39 b Fo(F)2552 4876 y Fi(\000)2607 4918 y Fj(1)p 2607 4934 V 2607 4991 a(2)2653 4876 y Fi(\001)2732 4957 y Fp(=)34 b(0)p Fg(,)k Fo(F)3036 4876 y Fi(\000)3092 4918 y Fj(3)p 3092 4934 V 3092 4991 a(4)3137 4876 y Fi(\001)3216 4957 y Fp(=)c(1)386 5092 y Fg(and)569 5012 y Fk(p)p 652 5012 248 4 v 80 x Fp(1)22 b Fk(\000)g Fo(F)14 b Fg(,)959 5008 y Fk(p)p 1042 5008 77 4 v 84 x Fo(F)f Fg(,)1178 5008 y Fk(p)p 1261 5008 100 4 v 84 x Fo(F)1338 5064 y Fn(0)1389 5092 y Fk(2)28 b Fo(C)1560 5056 y Fn(1)1635 5092 y Fg(,)h(which)f(is)g(stable)g(under)h(the)f(maps)g Fo(F)41 b Fk(!)27 b Fo(F)3308 5056 y Fm(m)386 5209 y Fg(and)40 b Fo(F)52 b Fk(!)38 b Fp(1)26 b Fk(\000)h Fp(\(1)22 b Fk(\000)g Fo(F)14 b Fp(\))1336 5160 y Fm(m)1403 5209 y Fp(;)40 b Fo(m)f Fk(2)g FC(N)p Fg(.)61 b(L)-5 b(et)41 b Fk(F)2124 5224 y Fn(\000)2223 5209 y Fg(denote)g(the)f(set)h(of)f (functions)386 5325 y Fo(F)449 5340 y Fn(\000)536 5325 y Fp(=)27 b(1)22 b Fk(\000)h Fo(F)873 5340 y Fj(+)967 5325 y Fg(wher)-5 b(e)34 b Fo(F)1305 5340 y Fj(+)1392 5325 y Fk(2)28 b(F)1558 5340 y Fj(+)1617 5325 y Fg(.)486 5506 y Fp(W)-8 b(e)32 b(shall)g(in)g(Section)g(5)g(use)g(a)g(mo)s (di\014cation)g(of)f(the)h(abstract)g(calculus)h([D,)386 5623 y(Lemma)g(A.3)g(\(b\)],)f(see)i(also)f([DG,)e(App)s(endix)k(C],)e ([G1,)f(App)s(endix])i(or)e([M\034].)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 386 259 a Fl(18)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y FC(Lemma)31 b(3.5.)36 b Fg(Supp)-5 b(ose)1375 434 y Fp(\026)1349 459 y Fo(H)36 b Fg(and)27 b Fo(B)34 b Fg(ar)-5 b(e)28 b(self-adjoint)f(op)-5 b(er)g(ators)27 b(on)h(a)g(c)-5 b(omplex)386 575 y(Hilb)g(ert)31 b(sp)-5 b(ac)g(e)30 b Fk(H)i Fg(,)f(and)g(that)g Fk(f)p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))28 b Fk(j)f Fo(t)h(>)f(t)2034 590 y Fj(0)2074 575 y Fk(g)k Fg(is)f(a)h(family)f(of)h(self-adjoint)e(op-)386 691 y(er)-5 b(ators)31 b(on)f Fk(H)j Fg(with)d(the)i(c)-5 b(ommon)29 b(domain)h Fk(D)s Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))27 b(=)h Fk(D)s Fp(\()p Fo(B)5 b Fp(\))p Fg(.)43 b(Supp)-5 b(ose)30 b(that)411 784 y Fp(\026)386 809 y Fo(H)47 b Fg(is)39 b(b)-5 b(ounde)g(d,)39 b(that)h(the)f(c)-5 b(ommutator)39 b(form)g Fo(i)2218 728 y Fi(\002)2285 784 y Fp(\026)2260 809 y Fo(H)7 b(;)17 b(B)5 b Fp(\()p Fo(t)p Fp(\))2582 728 y Fi(\003)2663 809 y Fg(de\014ne)-5 b(d)38 b(on)h Fk(D)s Fp(\()p Fo(B)5 b Fp(\))386 927 y Fg(is)39 b(a)g(symmetric)g(op)-5 b(er)g(ator)39 b(with)h(same)e(\(op)-5 b(er)g(ator\))39 b(domain)f Fk(D)s Fp(\()p Fo(B)5 b Fp(\))39 b Fg(and)g(that)386 1051 y(the)c Fk(B)s Fp(\()p Fk(H)q Fp(\)-v)-5 b(alued)35 b Fg(function)g Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\()p Fo(B)27 b Fk(\000)c Fo(i)p Fp(\))2002 1003 y Fn(\000)p Fj(1)2131 1051 y Fg(is)34 b(c)-5 b(ontinuously)35 b(di\013er)-5 b(entiable.)386 1168 y(Then)486 1284 y(\(A\))49 b(F)-7 b(or)31 b(any)g(given)g Fo(F)41 b Fk(2)29 b Fo(C)1576 1248 y Fn(1)1569 1309 y Fj(0)1650 1284 y Fp(\()p FC(R)p Fp(\))i Fg(we)g(let)2138 1259 y Fp(~)2116 1284 y Fo(F)41 b Fk(2)28 b Fo(C)2391 1248 y Fn(1)2384 1309 y Fj(0)2466 1284 y Fp(\()p FC(C)p Fp(\))j Fg(denote)g(an)g(almost)386 1400 y(analytic)k(extension.)43 b(In)34 b(p)-5 b(articular)539 1673 y Fo(F)14 b Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))28 b(=)1028 1606 y(1)p 1023 1651 59 4 v 1023 1742 a Fo(\031)1109 1538 y Fi(Z)1164 1763 y Fd(C)1243 1563 y Fi(\020)1315 1647 y Fp(\026)1303 1673 y Fo(@)1382 1648 y Fp(~)1360 1673 y Fo(F)1436 1563 y Fi(\021)1496 1673 y Fp(\()p Fo(z)t Fp(\))q(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)t Fp(\))2059 1625 y Fn(\000)p Fj(1)2154 1673 y Fo(dudv)t(;)115 b(z)32 b Fp(=)c Fo(u)21 b Fp(+)h Fo(iv)t(:)153 b Fp(\(3.10\))486 1956 y Fg(The)24 b Fk(B)s Fp(\()q Fk(H)q Fp(\))p Fg(-value)-5 b(d)24 b(function)h Fo(F)14 b Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))25 b Fg(is)g(c)-5 b(ontinuously)26 b(di\013er)-5 b(entiable,)25 b(and)386 2075 y(intr)-5 b(o)g(ducing)34 b(the)h(Heisenb)-5 b(er)g(g)34 b(derivative)g FC(D)28 b Fp(=)2231 2036 y Fm(d)p 2218 2052 62 4 v 2218 2109 a(dt)2312 2075 y Fp(+)22 b Fo(i)2443 1994 y Fi(\002)2510 2050 y Fp(\026)2485 2075 y Fo(H)8 b(;)17 b Fk(\001)2646 1994 y Fi(\003)2687 2075 y Fg(,)34 b(the)h(form)1328 2297 y Fo(d)p 1310 2342 86 4 v 1310 2433 a(dt)1406 2365 y(F)14 b Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))22 b(+)g Fo(i)1902 2284 y Fi(\002)1969 2340 y Fp(\026)1944 2365 y Fo(H)7 b(;)17 b(F)d Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))2419 2284 y Fi(\003)386 2621 y Fg(is)35 b(given)f(by)h(the)f(b) -5 b(ounde)g(d)35 b(op)-5 b(er)g(ator)432 2894 y FC(D)p Fo(F)14 b Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))27 b(=)h Fk(\000)1084 2827 y Fp(1)p 1079 2871 59 4 v 1079 2962 a Fo(\031)1165 2758 y Fi(Z)1220 2984 y Fd(C)1300 2783 y Fi(\020)1371 2868 y Fp(\026)1359 2894 y Fo(@)1438 2869 y Fp(~)1416 2894 y Fo(F)1493 2783 y Fi(\021)1552 2894 y Fp(\()p Fo(z)t Fp(\))q(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)t Fp(\))2116 2846 y Fn(\000)p Fj(1)2210 2894 y Fp(\()p FC(D)p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\)\()p Fo(B)g Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)t Fp(\))3000 2846 y Fn(\000)p Fj(1)3094 2894 y Fo(dudv)t(:)3125 3067 y Fp(\(3.11\))486 3183 y Fg(In)42 b(p)-5 b(articular)43 b(if)g FC(D)p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))44 b Fg(is)f(b)-5 b(ounde)g(d)42 b(then)h(for)g(any)h Fo(\017)f(>)g Fp(0)g Fg(\(with)g Fk(h)p Fo(z)t Fk(i)h Fp(=)386 3328 y(\(1)22 b(+)g Fk(j)p Fo(z)t Fk(j)698 3292 y Fj(2)737 3328 y Fp(\))785 3249 y Fh(1)p 785 3261 31 3 v 785 3302 a(2)830 3328 y Fg(\))515 3586 y Fk(k)p FC(D)p Fo(F)14 b Fp(\()o Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fk(k)28 b(\024)g Fo(C)1246 3601 y Fm(\017)1295 3586 y Fp(sup)1298 3668 y Fm(z)s Fn(2)p Fd(C)1458 3476 y Fi(\020)1518 3586 y Fk(h)p Fo(z)t Fk(i)1645 3538 y Fm(\017)p Fj(+2)1768 3586 y Fk(j)17 b Fp(Im)f Fo(z)t Fk(j)2022 3545 y Fn(\000)p Fj(2)2117 3586 y Fk(j)2145 3505 y Fi(\000)2203 3560 y Fp(\026)2191 3586 y Fo(@)2270 3561 y Fp(~)2247 3586 y Fo(F)2324 3505 y Fi(\001)2370 3586 y Fp(\()p Fo(z)t Fp(\))p Fk(j)2523 3476 y Fi(\021)2583 3586 y Fk(jj)p FC(D)p Fo(B)5 b Fp(\()o Fo(t)p Fp(\))p Fk(jj)p Fo(:)128 b Fp(\(3.12\))486 3875 y Fg(\(B\))49 b(Supp)-5 b(ose)42 b(in)h(addition)g(that)g(we)g(c)-5 b(an)43 b(split)g FC(D)p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))43 b(=)g Fo(D)s Fp(\()p Fo(t)p Fp(\))29 b(+)f Fo(D)3196 3890 y Fm(r)3234 3875 y Fp(\()p Fo(t)p Fp(\))p Fg(,)386 3991 y(wher)-5 b(e)38 b Fo(D)s Fp(\()p Fo(t)p Fp(\))g Fg(and)g Fo(D)1172 4006 y Fm(r)1210 3991 y Fp(\()p Fo(t)p Fp(\))h Fg(ar)-5 b(e)39 b(symmetric)f(op)-5 b(er)g(ators)38 b(on)g Fk(D)s Fp(\()p Fo(B)5 b Fp(\))39 b Fg(and)f(that)h(the)386 4112 y(form)k Fo(i)663 4076 y Fm(k)706 4112 y Fo(ad)808 4076 y Fm(k)808 4141 y(B)s Fj(\()q Fm(t)p Fj(\))949 4112 y Fp(\()p Fo(D)s Fp(\()p Fo(t)p Fp(\)\))h(=)g Fo(i)1417 4031 y Fi(\002)1458 4112 y Fo(i)1491 4076 y Fm(k)r Fn(\000)p Fj(1)1625 4112 y Fo(ad)1727 4071 y Fm(k)r Fn(\000)p Fj(1)1727 4143 y Fm(B)s Fj(\()p Fm(t)p Fj(\))1868 4112 y Fp(\()o Fo(D)s Fp(\()p Fo(t)p Fp(\)\))p Fo(;)17 b(B)5 b Fp(\()p Fo(t)p Fp(\))2372 4031 y Fi(\003)2457 4112 y Fg(for)44 b Fo(k)j Fp(=)d(1)f Fg(de\014ne)-5 b(d)43 b(on)386 4247 y Fk(D)s Fp(\()o Fo(B)5 b Fp(\))46 b Fg(is)g(a)g(symmetric)f(op)-5 b(er)g(ator)46 b(on)f Fk(D)s Fp(\()p Fo(B)5 b Fp(\))p Fg(;)51 b Fo(ad)2326 4211 y Fj(0)2326 4277 y Fm(B)s Fj(\()q Fm(t)p Fj(\))2467 4247 y Fp(\()p Fo(D)s Fp(\()p Fo(t)p Fp(\)\))d(=)g Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fg(.)78 b(\(No)386 4376 y(assumption)36 b(is)h(made)f(for)h(the)g(form)f(when)h Fo(k)d Fp(=)e(2)p Fg(.\))51 b(Then)36 b(the)h(c)-5 b(ontribution)386 4493 y(fr)g(om)34 b Fo(D)s Fp(\()p Fo(t)p Fp(\))h Fg(to)g(\(3.11\))f(c) -5 b(an)34 b(b)-5 b(e)35 b(written)g(as)665 4863 y Fk(\000)757 4795 y Fp(1)p 752 4840 59 4 v 752 4931 a Fo(\031)838 4727 y Fi(Z)893 4953 y Fd(C)956 4782 y Fi(\000)1014 4836 y Fp(\026)1002 4863 y Fo(@)1081 4838 y Fp(~)1059 4863 y Fo(F)1136 4782 y Fi(\001)1181 4863 y Fp(\()p Fo(z)t Fp(\))q(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)t Fp(\))1745 4814 y Fn(\000)p Fj(1)1839 4863 y Fo(D)s Fp(\()p Fo(t)p Fp(\)\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)t Fp(\))2471 4814 y Fn(\000)p Fj(1)2566 4863 y Fo(dudv)984 5122 y Fp(=)1098 5054 y(1)p 1098 5099 49 4 v 1098 5190 a(2)1156 5122 y(\()p Fo(F)1271 5080 y Fn(0)1294 5122 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fo(D)s Fp(\()p Fo(t)p Fp(\))22 b(+)g Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fo(F)2147 5080 y Fn(0)2170 5122 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\)\))22 b(+)g Fo(R)2668 5137 y Fj(1)2708 5122 y Fp(\()p Fo(t)p Fp(\);)279 b(\(3.13\))732 5363 y Fo(R)806 5378 y Fj(1)845 5363 y Fp(\()p Fo(t)p Fp(\))28 b(=)1127 5296 y(1)p 1098 5340 108 4 v 1098 5431 a(2)p Fo(\031)1232 5227 y Fi(Z)1287 5453 y Fd(C)1367 5282 y Fi(\000)1425 5337 y Fp(\026)1412 5363 y Fo(@)1491 5338 y Fp(~)1469 5363 y Fo(F)1546 5282 y Fi(\001)1592 5363 y Fp(\()p Fo(z)t Fp(\)\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))23 b Fk(\000)f Fo(z)t Fp(\))2155 5314 y Fn(\000)p Fj(2)1576 5581 y Fk(\001)g Fo(ad)1728 5540 y Fj(2)1728 5606 y Fm(B)s Fj(\()q Fm(t)p Fj(\))1869 5581 y Fp(\()p Fo(D)s Fp(\()p Fo(t)p Fp(\)\)\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)t Fp(\))2577 5533 y Fn(\000)p Fj(2)2672 5581 y Fo(dudv)t(:)p eop end %%Page: 19 19 TeXDict begin 19 18 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(19)386 459 y Fg(F)-7 b(or)34 b(al)5 b(l)34 b Fo(f)39 b Fk(2)28 b Fo(C)965 423 y Fn(1)958 483 y Fj(0)1039 459 y Fp(\()p FC(R)p Fp(\))776 580 y Fj(1)p 776 597 36 4 v 776 654 a(2)821 539 y Fi(\000)867 620 y Fo(f)926 578 y Fj(2)965 620 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fo(D)s Fp(\()p Fo(t)p Fp(\))22 b(+)g Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fo(f)1800 578 y Fj(2)1839 620 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))2105 539 y Fi(\001)794 771 y Fp(=)27 b Fo(f)11 b Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fo(f)11 b Fp(\()o Fo(B)5 b Fp(\()p Fo(t)p Fp(\))q(\))22 b(+)g Fo(R)1936 786 y Fj(2)1975 771 y Fp(\()p Fo(t)p Fp(\);)1012 b(\(3.14\))541 983 y Fo(R)615 998 y Fj(2)655 983 y Fp(\()p Fo(t)p Fp(\))28 b(=)956 915 y(1)p 907 960 148 4 v 907 1051 a(2)p Fo(\031)1015 1022 y Fj(2)1081 847 y Fi(Z)1136 1073 y Fd(C)1216 847 y Fi(Z)1271 1073 y Fd(C)1350 902 y Fi(\000)1408 956 y Fp(\026)1396 983 y Fo(@)1474 956 y Fp(~)1453 983 y Fo(f)1512 902 y Fi(\001)1557 983 y Fp(\()p Fo(z)1640 998 y Fj(2)1680 983 y Fp(\))1718 902 y Fi(\000)1776 956 y Fp(\026)1764 983 y Fo(@)1842 956 y Fp(~)1821 983 y Fo(f)1879 902 y Fi(\001)1925 983 y Fp(\()p Fo(z)2008 998 y Fj(1)2048 983 y Fp(\)\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)2481 998 y Fj(2)2520 983 y Fp(\))2558 934 y Fn(\000)p Fj(1)2653 983 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(z)3048 998 y Fj(1)3087 983 y Fp(\))3125 934 y Fn(\000)p Fj(1)766 1201 y Fo(ad)868 1160 y Fj(2)868 1226 y Fm(B)s Fj(\()q Fm(t)p Fj(\))1009 1201 y Fp(\()p Fo(D)s Fp(\()o Fo(t)p Fp(\))q(\))o(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))23 b Fk(\000)f Fo(z)1674 1216 y Fj(1)1714 1201 y Fp(\))1752 1153 y Fn(\000)p Fj(1)1846 1201 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\))23 b Fk(\000)f Fo(z)2241 1216 y Fj(2)2281 1201 y Fp(\))2319 1153 y Fn(\000)p Fj(1)2413 1201 y Fo(du)2520 1216 y Fj(1)2559 1201 y Fo(dv)2657 1216 y Fj(1)2696 1201 y Fo(du)2803 1216 y Fj(2)2842 1201 y Fo(dv)2940 1216 y Fj(2)2979 1201 y Fo(:)486 1368 y Fg(\(C\))92 b(Supp)-5 b(ose)42 b(in)h(addition)f(to)i(pr)-5 b(evious)42 b(assumptions)g(that) i(for)f(al)5 b(l)43 b Fo(t)g(>)386 1485 y(t)421 1500 y Fj(0)500 1485 y Fg(the)c(form)f Fo(i)p Fp([)p Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fo(;)17 b(B)5 b Fp(\()p Fo(t)p Fp(\)])39 b Fg(extends)g(fr)-5 b(om)38 b Fk(D)s Fp(\()p Fo(B)5 b Fp(\))39 b Fg(to)g(a)g(b)-5 b(ounde)g(d)38 b(self-adjoint)386 1601 y(op)-5 b(er)g(ator.)71 b(Similarly)43 b(supp)-5 b(ose)43 b(the)h(op)-5 b(er)g(ator)43 b Fo(D)2271 1616 y Fm(r)2309 1601 y Fp(\()p Fo(t)p Fp(\))h Fg(extends)f(to)h(a)f(b)-5 b(ounde)g(d)386 1717 y(self-adjoint)39 b(op)-5 b(er)g(ator.)61 b(Then)39 b(for)i(al)5 b(l)40 b Fo(F)51 b Fk(2)38 b(F)2193 1732 y Fj(+)2292 1717 y Fg(the)j Fk(B)s Fp(\()p Fk(H)q Fp(\))p Fg(-value)-5 b(d)40 b(function)386 1841 y Fo(F)14 b Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\)\()p Fo(B)27 b Fk(\000)c Fo(i)p Fp(\))1039 1793 y Fn(\000)p Fj(1)1165 1841 y Fg(is)31 b(c)-5 b(ontinuously)32 b(di\013er)-5 b(entiable,)31 b(and)g(ther)-5 b(e)32 b(is)f(an)g(almost)386 1958 y(analytic)k(extension)e(with)1099 2038 y Fi(\014)1099 2098 y(\014)1132 2042 y(\000)1190 2096 y Fp(\026)1178 2123 y Fo(@)1257 2098 y Fp(~)1235 2123 y Fo(F)1312 2042 y Fi(\001)1357 2123 y Fp(\()p Fo(z)t Fp(\))1483 2038 y Fi(\014)1483 2098 y(\014)1544 2123 y Fk(\024)28 b Fo(C)1719 2138 y Fm(k)1762 2123 y Fk(h)o Fo(z)t Fk(i)1889 2074 y Fn(\000)p Fj(1)p Fn(\000)p Fm(k)2077 2123 y Fk(j)17 b Fp(Im)f Fo(z)t Fk(j)2331 2082 y Fm(k)2374 2123 y Fp(;)52 b Fk(2)28 b FC(N)p Fo(;)463 b Fp(\(3.15\))386 2282 y Fg(yielding)34 b(the)h(r)-5 b(epr)g(esentation)436 2453 y FC(D)p Fo(F)14 b Fp(\()o Fo(B)5 b Fp(\()p Fo(t)p Fp(\))q(\))27 b(=)h Fo(F)1073 2412 y Fn(0)1102 2385 y Fh(1)p 1101 2397 31 3 v 1101 2438 a(2)1146 2453 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fo(F)1684 2412 y Fn(0)1713 2385 y Fh(1)p 1713 2397 V 1713 2438 a(2)1757 2453 y Fp(\()p Fo(B)g Fp(\()p Fo(t)p Fp(\)\))21 b(+)f Fo(R)2214 2468 y Fj(1)2254 2453 y Fp(\()p Fo(t)p Fp(\))h(+)f Fo(R)2556 2468 y Fj(2)2596 2453 y Fp(\()p Fo(t)p Fp(\))g(+)h Fo(R)2898 2468 y Fj(3)2937 2453 y Fp(\()p Fo(t)p Fp(\))q Fo(;)49 b Fp(\(3.16\))386 2621 y Fg(wher)-5 b(e)28 b Fo(R)729 2636 y Fj(1)769 2621 y Fp(\()p Fo(t)p Fp(\))h Fg(is)g(given)f(by)h(\(3.13\),)g Fo(R)1770 2636 y Fj(2)1810 2621 y Fp(\()p Fo(t)p Fp(\))g Fg(by)g(\(3.14\))f(with)h Fo(f)38 b Fp(=)2755 2537 y Fk(p)p 2838 2537 100 4 v 84 x Fo(F)2915 2592 y Fn(0)2967 2621 y Fg(and)28 b Fo(R)3224 2636 y Fj(3)3264 2621 y Fp(\()p Fo(t)p Fp(\))386 2738 y Fg(is)35 b(the)f(c)-5 b(ontribution)35 b(fr)-5 b(om)35 b Fo(D)1511 2753 y Fm(r)1548 2738 y Fp(\()p Fo(t)p Fp(\))g Fg(to)g(\(3.11\).)386 2913 y(R)-5 b(emarks)42 b Fp(3.6)p Fg(.)534 3051 y Fp(\(1\))f(The)24 b(left)f(hand)h(side)g(of)e(\(3.16\))g(is)i(initially)f(de\014ned)i(as) e(a)g(form)f(on)h Fk(D)s Fp(\()p Fo(B)5 b Fp(\))700 3167 y(while)36 b(the)e(terms)h(on)f(the)g(righ)m(t)h(hand)f(side)h(are)f(b) s(ounded)h(op)s(erators.)700 3283 y(W)-8 b(e)42 b(shall)f(use)h(the)g (stated)g(represen)m(tation)g(form)m(ulas)g(for)e(b)s(ounding)700 3399 y(these)26 b(op)s(erators)e(in)g(an)g(application)h(in)f(the)h (pro)s(of)e(of)h(Prop)s(osition)g(5.1;)700 3516 y(this)35 b(will)f(b)s(e)g(in)g(the)g(spirit)g(of)f(\(3.12\))g(although)g (somewhat)i(more)f(so-)700 3632 y(phisticated.)534 3748 y(\(2\))41 b(There)32 b(are)e(v)m(ersions)i(of)e(Lemma)g(3.5)g(without) h(the)f(assumption)3181 3723 y(\026)3156 3748 y Fo(H)37 b Fp(b)s(e)700 3864 y(b)s(ounded;)d(they)f(are)g(not)f(needed)j(in)d (this)i(pap)s(er.)1410 4068 y(4.)48 b Fo(t)1569 4032 y Fn(\000)p Fm(\016)1662 4068 y Fq({localiza)-7 b(tion)486 4243 y Fp(Let)41 b Fo( )46 b Fp(=)d Fo(f)11 b Fp(\()o Fo(H)d Fp(\))p Fo( )45 b Fp(b)s(e)c(an)m(y)h(state)g(ob)s(eying)h (\(1.8\))e(and)g(\(1.9\))g(with)g Fo(f)52 b Fp(sup-)386 4359 y(p)s(orted)c(in)g(a)f(v)m(ery)i(small)g(neigh)m(b)s(orho)s(o)s(d) e(of)h Fo(E)2264 4374 y Fj(0)2351 4359 y Fp(\(in)g(agreemen)m(t)h(with) f(the)386 4475 y(smallness)39 b(of)d(the)h(neigh)m(b)s(orho)s(o)s(d)g Fo(I)1767 4490 y Fj(0)1843 4475 y Fp(of)f(Theorem)i(1.1\).)55 b(Let)37 b Fo(g)2845 4490 y Fj(1)2884 4475 y Fo(;)20 b Fp(~)-52 b Fo(g)2975 4490 y Fj(1)3014 4475 y Fo(;)17 b(g)3105 4490 y Fj(2)3144 4475 y Fo(;)j Fp(~)-52 b Fo(g)3235 4490 y Fj(2)3308 4475 y Fk(2)386 4591 y Fo(C)463 4555 y Fn(1)456 4616 y Fj(0)538 4591 y Fp(\()p FC(R)660 4555 y Fm(n)706 4591 y Fp(\))33 b(b)s(e)f(giv)m(en)i(as)f(in)g(\(3.2\))f (and)g(\(3.5\).)43 b(In)33 b(particular)g(w)m(e)h(ha)m(v)m(e)799 4751 y Fo(g)846 4766 y Fj(1)885 4751 y Fp(\()p Fo(k)s Fp(\()p Fo(E)6 b Fp(\))p Fo(!)t Fp(\()o Fo(E)g Fp(\)\))p Fo(f)11 b Fp(\()p Fo(E)6 b Fp(\))27 b(=)h Fo(f)11 b Fp(\()p Fo(E)6 b Fp(\))p Fo(;)44 b(g)2062 4766 y Fj(2)2101 4751 y Fp(\()p Fo(\030)5 b Fp(\()o Fo(E)h Fp(\)\))p Fo(f)11 b Fp(\()p Fo(E)6 b Fp(\))28 b(=)f Fo(f)11 b Fp(\()p Fo(E)6 b Fp(\))p Fo(:)486 4910 y Fp(Consider)34 b(for)e Fo(t;)17 b(\024)27 b Fk(\025)h Fp(1)33 b(sym)m(b)s(ols)943 5069 y Fo(a)28 b Fp(=)g Fo(a)1177 5084 y Fm(t;\024)1267 5069 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(F)1683 5084 y Fj(+)1743 4988 y Fi(\000)1788 5069 y Fo(\024q)1891 5028 y Fn(\000)1950 5069 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2173 4988 y Fi(\001)2222 5069 y Fp(~)-53 b Fo(g)2265 5084 y Fj(1)2305 4988 y Fi(\000)2350 5069 y Fo(t)2385 5028 y Fn(\000)p Fj(1)2480 5069 y Fo(x)2535 4988 y Fi(\001)2584 5069 y Fp(~)h Fo(g)2628 5084 y Fj(2)2667 5069 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(;)357 b Fp(\(4.1\))386 5231 y(where)39 b Fo(F)736 5246 y Fj(+)833 5231 y Fp(is)g(giv)m(en)g(as)f(in)g (De\014nition)g(3.4)g(and)g Fo(q)2305 5195 y Fn(\000)2401 5231 y Fp(is)h(built)f(from)g(the)g Fo(q)3199 5195 y Fn(\000)3296 5231 y Fp(of)386 5347 y(\(2.10\))29 b(b)m(y)i(writing)f Fo(q)1178 5311 y Fn(\000)1264 5347 y Fp(=)e Fo(q)1415 5311 y Fn(\000)1474 5347 y Fp(\()p Fo(w)s Fp(\()o Fo(E)6 b Fp(\))p Fo(;)17 b(E)6 b Fp(\))29 b(and)h(substituting)h(for)f Fo(E)35 b Fp(the)30 b(sym)m(b)s(ol)386 5464 y Fo(h)p Fp(\()p Fo(r)524 5479 y Fj(0)569 5464 y Fp(^)-55 b Fo(x)q(;)17 b(\030)5 b Fp(\))31 b(cf.)44 b(\(3.2\),)1229 5623 y Fo(q)31 b Fp(=)d Fo(q)1454 5582 y Fn(\000)1513 5623 y Fp(\()p Fo(w)s Fp(\()o Fo(h)p Fp(\()p Fo(r)1799 5638 y Fj(0)1845 5623 y Fp(^)-55 b Fo(x;)17 b(\030)5 b Fp(\))o(\))p Fo(;)17 b(h)p Fp(\()p Fo(r)2243 5638 y Fj(0)2288 5623 y Fp(^)-55 b Fo(x)q(;)17 b(\030)5 b Fp(\))o(\))p Fo(:)642 b Fp(\(4.2\))p eop end %%Page: 20 20 TeXDict begin 20 19 bop 386 259 a Fl(20)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)486 459 y Fp(W)-8 b(e)30 b(shall)h(consider)h Fo(\024)c Fk(2)g Fp([1)p Fo(;)17 b(t)1588 423 y Fm(\027)1631 459 y Fp(])30 b(with)h Fo(\027)j(>)28 b Fp(0.)42 b(T)-8 b(o)31 b(ha)m(v)m(e)g(a)f(go)s(o)s(d)f(calculus)j (for)386 575 y(the)h(sym)m(b)s(ol)h Fo(a)e Fp(w)m(e)i(need)g Fo(\027)g(<)27 b Fp(1)p Fo(=)p Fp(2.)43 b(Notice)33 b(that)1418 750 y Fo(a)1469 765 y Fm(t;\024)1586 750 y Fk(2)c Fo(S)1741 765 y Fm(unif)1894 669 y Fi(\000)1939 750 y Fp(1)p Fo(;)17 b(g)2083 703 y Fj(1)p Fn(\000)p Fm(\027;\027)2079 773 y(t)2270 669 y Fi(\001)2316 750 y Fo(:)831 b Fp(\(4.3\))486 927 y(Denoting)31 b(b)m(y)h Fk(h\001i)1145 956 y Fm(t)1206 927 y Fp(the)g(exp)s(ectation)h(in)e(the)h(state)g Fo( )t Fp(\()p Fo(t)p Fp(\))c(=)g Fo(e)2770 891 y Fn(\000)p Fm(itH)2941 927 y Fo( )36 b Fp(w)m(e)c(ha)m(v)m(e)386 1043 y(the)h(follo)m(wing)g(lo)s(calization.)386 1224 y FC(Lemma)39 b(4.1.)j Fg(F)-7 b(or)34 b(al)5 b(l)34 b Fo(\027)g Fk(2)29 b Fp(\()o(0)p Fo(;)17 b Fp(2)p Fo(=)p Fp(5\))1276 1313 y Fi(\012)1323 1394 y Fo(a)1374 1353 y Fm(w)1374 1418 y(t;t)1444 1399 y Ff(\027)1487 1394 y Fp(\()p Fo(x;)g(p)p Fp(\))1711 1313 y Fi(\013)1758 1435 y Fm(t)1815 1394 y Fk(!)28 b Fp(0)f(for)32 b Fo(t)c Fk(!)f(1)p Fo(:)689 b Fp(\(4.4\))386 1583 y Fg(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)33 b(shall)g(use)h(a)e(sc)m(heme)j(of)d(pro) s(of)g(from)g([D].)g(Let)669 1753 y Fo(A)742 1768 y Fm(t;\024)860 1753 y Fp(=)27 b Fo(L)1029 1768 y Fj(1)1069 1753 y Fp(\()p Fo(t)p Fp(\))1180 1704 y Fn(\003)1219 1753 y Fo(a)1270 1712 y Fm(w)1270 1777 y(t;\024)1361 1753 y Fp(\()o Fo(x;)17 b(p)p Fp(\))p Fo(L)1650 1768 y Fj(1)1690 1753 y Fp(\()p Fo(t)p Fp(\);)115 b Fo(L)2009 1768 y Fj(1)2048 1753 y Fp(\()p Fo(t)p Fp(\))28 b(=)g Fo(g)2338 1768 y Fj(1)2377 1672 y Fi(\000)2423 1753 y Fo(t)2458 1712 y Fn(\000)p Fj(1)2552 1753 y Fo(x)2607 1672 y Fi(\001)2653 1753 y Fo(g)2700 1768 y Fj(2)2739 1753 y Fp(\()p Fo(p)p Fp(\))p Fo(:)283 b Fp(\(4.5\))486 1925 y(F)-8 b(rom)33 b(\(1.10\))g(and)i(the)f (calculus)i(of)e(pseudo)s(di\013eren)m(tial)i(op)s(erators)e(w)m(e)h (im-)386 2042 y(mediately)f(conclude)g(that)e(for)g(\014xed)i Fo(\024)1382 2210 y Fk(h)o Fo(A)1493 2225 y Fm(s;\024)1591 2210 y Fk(i)1629 2242 y Fm(s)1694 2210 y Fk(!)27 b Fp(0)32 b(for)g Fo(s)c Fk(!)f(1)p Fo(;)386 2378 y Fp(yielding)1298 2555 y Fk(\000h)q Fo(A)1488 2570 y Fm(t;\024)1578 2555 y Fk(i)1616 2587 y Fm(t)1674 2555 y Fp(=)1777 2419 y Fi(Z)1877 2445 y Fn(1)1833 2645 y Fm(t)1968 2555 y Fk(h)p FC(D)p Fo(A)2166 2570 y Fm(s;\024)2263 2555 y Fk(i)2302 2587 y Fm(s)2339 2555 y Fo(ds;)711 b Fp(\(4.6\))386 2770 y(where)33 b FC(D)f Fp(refers)h(to)e(the)i(Heisen)m(b)s(erg)g(deriv)-5 b(ativ)m(e)34 b FC(D)27 b Fp(=)2519 2731 y Fm(d)p 2503 2747 69 4 v 2503 2804 a(ds)2603 2770 y Fp(+)21 b Fo(i)p Fp([)p Fo(H)r(;)c Fk(\001)p Fp(])o(.)44 b(W)-8 b(e)32 b(shall)386 2887 y(sho)m(w)26 b(that)g(the)f(exp)s(ectation)i(of)e FC(D)p Fo(A)1767 2902 y Fm(s;\024)1889 2887 y Fp(is)h(essen)m(tially)i (p)s(ositiv)m(e)f(\(in)e(agreemen)m(t)386 3009 y(with)40 b(\(2.12\)\).)63 b(Up)40 b(to)f(terms)h Fo(O)s Fp(\()o Fo(s)1725 2973 y Fn(\0001)1855 3009 y Fp(\))f(w)m(e)i(ma)m(y)f(replace) g FC(D)g Fp(b)m(y)g FC(D)2992 3024 y Fm(s)3068 3009 y Fp(=)3209 2970 y Fm(d)p 3193 2986 V 3193 3043 a(ds)3299 3009 y Fp(+)386 3126 y Fo(i)p Fp([)p Fo(h)502 3090 y Fm(w)502 3151 y(s)559 3126 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(;)g Fk(\001)p Fp(])o(,)33 b(cf.)44 b(Remark)33 b(3.3.)43 b(First)33 b(w)m(e)g(notice)g(that)638 3296 y Fo(g)685 3311 y Fj(2)724 3296 y Fp(\()p Fo(p)p Fp(\))p Fo(g)896 3311 y Fj(1)935 3215 y Fi(\000)981 3296 y Fo(s)1027 3255 y Fn(\000)p Fj(1)1121 3296 y Fo(x)1176 3215 y Fi(\001\000)1268 3296 y FC(D)1354 3311 y Fm(s)1391 3296 y Fo(a)1442 3255 y Fm(w)1442 3321 y(s;\024)1539 3296 y Fp(\()p Fo(x;)17 b(p)p Fp(\))1763 3215 y Fi(\001)1809 3296 y Fo(g)1856 3311 y Fj(1)1895 3215 y Fi(\000)1941 3296 y Fo(s)1987 3255 y Fn(\000)p Fj(1)2081 3296 y Fo(x)2136 3215 y Fi(\001)2182 3296 y Fo(g)2229 3311 y Fj(2)2268 3296 y Fp(\()p Fo(p)p Fp(\))28 b Fk(\025)g(\000)p Fo(C)7 b(s)2726 3255 y Fj(5)p Fm(\027)t Fn(\000)p Fj(3)2895 3296 y Fo(;)252 b Fp(\(4.7\))386 3469 y(where)34 b Fo(C)g(>)28 b Fp(0)k(is)h(indep)s(enden)m(t)i(of)d Fo(\024)c Fk(2)g Fp([1)p Fo(;)17 b(t)2052 3432 y Fm(\027)2095 3469 y Fp(].)486 3585 y(This)33 b(b)s(ound)g(follo)m(ws)h(from)e(the)h (calculus.)45 b(The)34 b(classical)g(P)m(oisson)g(brac)m(k)m(et)386 3701 y(con)m(tributes)52 b(b)m(y)f(a)g(p)s(ositiv)m(e)g(sym)m(b)s(ol)h (when)g(di\013eren)m(tiating)f Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\).)97 b(The)386 3817 y(F)-8 b(e\013erman-Phong)25 b(inequalit)m(y)i(\(see)f([H\177)-49 b(o,)27 b(Theorem)f(18.6.8)e(and)i (Lemma)f(18.6.)386 3965 y(10]\))31 b(for)g(this)h(term)g(yields)i(the)e (lo)m(w)m(er)g(b)s(ound)g Fo(O)2221 3854 y Fi(\020)2280 3965 y Fo(s)2326 3929 y Fm(\027)t Fn(\000)p Fj(1)2459 3965 y Fp(\()p Fo(s)2543 3929 y Fj(2)p Fm(\027)t Fn(\000)p Fj(1)2712 3965 y Fp(\))2750 3912 y Fj(2)2789 3854 y Fi(\021)2876 3965 y Fp(=)c Fo(O)s Fp(\()o Fo(s)3141 3929 y Fj(5)p Fm(\027)t Fn(\000)p Fj(3)3310 3965 y Fp(\).)486 4113 y(Hence)33 b(\(uniformly)h(in)f Fo(\024)p Fp(\))889 4282 y FC(D)p Fo(A)1048 4297 y Fm(s;\024)1172 4282 y Fk(\025)28 b(f)p Fo(T)36 b Fp(+)22 b Fo(T)1589 4241 y Fn(\003)1628 4282 y Fk(g)g(\000)h Fo(C)7 b(s)1923 4241 y Fj(5)p Fm(\027)t Fn(\000)p Fj(3)2091 4282 y Fp(;)889 4443 y Fo(T)41 b Fp(=)27 b Fo(g)1137 4458 y Fj(2)1177 4443 y Fp(\()p Fo(p)p Fp(\))o Fo(g)1348 4458 y Fj(1)1388 4362 y Fi(\000)1433 4443 y Fo(s)1479 4402 y Fn(\000)p Fj(1)1574 4443 y Fo(x)1629 4362 y Fi(\001)1675 4443 y Fo(a)1726 4402 y Fm(w)1726 4468 y(s;\024)1823 4443 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p FC(D)2133 4458 y Fm(s)2170 4362 y Fi(\000)2215 4443 y Fo(g)2262 4458 y Fj(1)2301 4362 y Fi(\000)2347 4443 y Fo(s)2393 4402 y Fn(\000)p Fj(1)2487 4443 y Fo(x)2542 4362 y Fi(\001)2588 4443 y Fo(g)2635 4458 y Fj(2)2675 4443 y Fp(\()o Fo(p)p Fp(\))2799 4362 y Fi(\001)2845 4443 y Fo(:)386 4611 y Fp(F)-8 b(or)46 b(the)h(con)m(tribution)g(from)g (the)g(\014rst)g(term)g(on)f(the)h(righ)m(t)g(hand)g(side)h(w)m(e)386 4728 y(in)m(v)m(ok)m(e)35 b(\(1.9\))d(after)g(symmetrizing.)46 b(W)-8 b(e)33 b(conclude)h(that)567 4815 y Fi(Z)666 4841 y Fn(1)622 5041 y Fm(t)757 4951 y Fk(h)p FC(D)p Fo(A)955 4966 y Fm(s;\024)1052 4951 y Fk(i)1091 4983 y Fm(s)1128 4951 y Fo(ds)27 b Fk(\025)h Fo(o)1404 4870 y Fi(\000)1450 4951 y Fo(t)1485 4910 y Fj(0)1525 4870 y Fi(\001)1592 4951 y Fk(\000)23 b Fo(C)7 b(t)1804 4910 y Fj(5)p Fm(\027)t Fn(\000)p Fj(2)2005 4951 y Fp(uniformly)34 b(in)e Fo(\024)c Fk(2)g Fp([)q(1)p Fo(;)17 b(t)2897 4910 y Fm(\027)2939 4951 y Fp(])p Fo(:)181 b Fp(\(4.8\))386 5170 y(Pic)m(k)34 b Fo(\024)28 b Fp(=)f Fo(t)826 5134 y Fm(\027)870 5170 y Fp(.)486 5286 y(By)33 b(com)m(bining)g(\(4.6\))f(and)h(\(4.8\))f(w)m (e)i(infer)f(that)1382 5455 y Fk(h)p Fo(A)1494 5470 y Fm(t;t)1564 5451 y Ff(\027)1608 5455 y Fk(i)1646 5487 y Fm(t)1704 5455 y Fk(!)27 b Fp(0)32 b(for)g Fo(t)c Fk(!)f(1)p Fo(;)386 5623 y Fp(and)33 b(therefore)g(\(4.4\).)2084 b Fe(\003)p eop end %%Page: 21 21 TeXDict begin 21 20 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(21)486 459 y Fp(Let)37 b Fo(q)712 423 y Fj(+)771 459 y Fo(;)17 b(q)862 423 y Fm(s)935 459 y Fp(and)38 b Fo(q)1177 423 y Fm(u)1259 459 y Fp(b)s(e)f(giv)m(en)i(as)e (in)g(\(2.10\))g(up)s(on)g(substituting)i Fo(E)k Fp(b)m(y)38 b(the)386 575 y(sym)m(b)s(ol)c Fo(h)p Fp(\()p Fo(r)858 590 y Fj(0)903 575 y Fp(^)-55 b Fo(x)q(;)17 b(\030)5 b Fp(\))o(,)32 b(cf.)44 b(the)33 b(use)h(of)e Fo(q)1780 539 y Fn(\000)1871 575 y Fp(ab)s(o)m(v)m(e.)44 b(W)-8 b(e)33 b(in)m(tro)s(duce)h(the)f(sym)m(b)s(ols)911 734 y Fo(a)962 692 y Fj(1)962 758 y Fm(t)1030 734 y Fp(=)27 b Fo(t)1168 692 y Fm(\027)t Fn(\000)p Fj(1)1302 734 y Fo(q)1349 692 y Fn(\000)1408 734 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(F)1707 692 y Fn(0)1693 758 y Fj(+)1752 653 y Fi(\000)1798 734 y Fo(t)1833 692 y Fm(\027)1876 734 y Fo(q)1923 692 y Fn(\000)1982 734 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2205 653 y Fi(\001)2254 734 y Fp(~)-53 b Fo(g)2297 749 y Fj(1)2336 653 y Fi(\000)2382 734 y Fo(t)2417 692 y Fn(\000)p Fj(1)2512 734 y Fo(x)2567 653 y Fi(\001)2616 734 y Fp(~)h Fo(g)2660 749 y Fj(2)2699 734 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(;)911 895 y(a)962 853 y Fj(2)962 919 y Fm(t)1030 895 y Fp(=)27 b Fo(t)1168 853 y Fm(\027)t Fn(\000)p Fj(1)1302 895 y Fo(q)1349 853 y Fj(+)1408 895 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(F)1707 853 y Fn(0)1693 919 y Fj(+)1752 814 y Fi(\000)1798 895 y Fo(t)1833 853 y Fm(\027)1876 895 y Fo(q)1923 853 y Fn(\000)1982 895 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2205 814 y Fi(\001)2254 895 y Fp(~)-53 b Fo(g)2297 910 y Fj(1)2336 814 y Fi(\000)2382 895 y Fo(t)2417 853 y Fn(\000)p Fj(1)2512 895 y Fo(x)2567 814 y Fi(\001)2616 895 y Fp(~)h Fo(g)2660 910 y Fj(2)2699 895 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(:)486 1052 y Fp(W)-8 b(e)29 b(get)h(the)f(follo)m(wing)h(in)m(tegral)g (estimate)g(from)f(the)h(ab)s(o)m(v)m(e)g(pro)s(of)f(emplo)m(y-)386 1168 y(ing)23 b(the)g(uniform)g(b)s(oundedness)i(of)d(the)h(family)g (of)f(\\propagation)g(observ)-5 b(ables")386 1284 y Fo(A)459 1299 y Fm(t;t)529 1280 y Ff(\027)572 1284 y Fp(,)32 b(cf.)43 b(a)32 b(standard)g(argumen)m(t)g(of)f(scattering)h(theory)g(see)h(for) e(example)i([D,)386 1400 y(Lemma)g(A.1)g(\(b\)].)386 1574 y FC(Lemma)39 b(4.2.)j Fg(In)34 b(the)h(state)g Fo( )1585 1589 y Fj(1)1625 1574 y Fp(\()p Fo(t)p Fp(\))28 b(=)f Fo(L)1933 1589 y Fj(1)1973 1574 y Fp(\()p Fo(t)p Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))866 1650 y Fi(Z)965 1676 y Fn(1)921 1875 y Fj(1)1057 1705 y Fi(\000)1102 1785 y Fk(j)1130 1705 y Fi(\012\000)1223 1785 y Fo(a)1274 1744 y Fj(1)1274 1810 y Fm(t)1313 1705 y Fi(\001)1359 1727 y Fm(w)1415 1785 y Fp(\()p Fo(x;)17 b(p)p Fp(\))1639 1705 y Fi(\013)1686 1824 y Fm(t)1716 1785 y Fk(j)22 b Fp(+)g Fk(j)1892 1705 y Fi(\012\000)1984 1785 y Fo(a)2035 1744 y Fj(2)2035 1810 y Fm(t)2075 1705 y Fi(\001)2121 1727 y Fm(w)2177 1785 y Fp(\()p Fo(x;)17 b(p)p Fp(\))2401 1705 y Fi(\013)2448 1824 y Fm(t)2478 1785 y Fk(j)2506 1705 y Fi(\001)2551 1785 y Fo(dt)28 b(<)f Fk(1)p Fo(:)386 2015 y Fg(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)45 b(substitute)i Fo(\024)h Fp(=)g Fo(t)1596 1979 y Fm(\027)1684 2015 y Fp(in)d(the)g(construction)h(\(4.5\).)79 b(Then)46 b(up)f(to)386 2132 y(in)m(tegrable)40 b(terms)h(the)e(left)h(hand)f(side)i(of)e (\(4.7\))g(\(with)g Fo(s)h Fp(=)f Fo(t)g Fp(\))g(is)h(giv)m(en)h(b)m(y) 386 2248 y Fo(c)428 2212 y Fm(w)428 2272 y(t)484 2248 y Fp(\()p Fo(x;)17 b(p)p Fp(\))33 b(with)469 2452 y Fo(c)511 2467 y Fm(t)541 2452 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(g)941 2467 y Fj(2)980 2452 y Fp(\()p Fo(\030)5 b Fp(\))1104 2404 y Fj(2)1143 2452 y Fo(g)1190 2467 y Fj(1)1229 2371 y Fi(\000)1275 2452 y Fo(t)1310 2411 y Fn(\000)p Fj(1)1404 2452 y Fo(x)1459 2371 y Fi(\001)1506 2394 y Fj(2)1036 2532 y Fi(\000)1082 2613 y Fo(\027)h(t)1171 2572 y Fm(\027)t Fn(\000)p Fj(1)1305 2613 y Fo(q)1352 2572 y Fn(\000)1411 2613 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h Fo(t)1788 2572 y Fm(\027)1832 2532 y Fi(\010)1890 2613 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)17 b(q)2260 2572 y Fn(\000)2318 2613 y Fp(\()p Fo(x;)g(\030)5 b Fp(\))2541 2532 y Fi(\011\001)2644 2613 y Fo(F)2721 2572 y Fn(0)2707 2638 y Fj(+)2767 2532 y Fi(\000)2812 2613 y Fo(t)2847 2572 y Fm(\027)2891 2613 y Fo(q)2938 2572 y Fn(\000)2997 2613 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\))3219 2532 y Fi(\001)3265 2613 y Fo(;)386 2776 y Fp(where)34 b Fk(f\001)p Fo(;)17 b Fk(\001g)31 b Fp(signi\014es)j(P)m(oisson)g(brac)m(k)m(et.)486 2892 y(W)-8 b(e)33 b(ha)m(v)m(e)g(the)g(b)s(ounds)h(for)e(some)h Fo(C)i(>)27 b Fp(0)33 b(and)f(all)h(large)f(enough)h Fo(t)572 3062 y(C)649 3020 y Fn(\000)p Fj(1)743 3062 y Fo(c)785 3077 y Fm(t)814 3062 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b Fk(\024)g Fo(g)1217 3077 y Fj(2)1256 3062 y Fp(\()p Fo(\030)5 b Fp(\))1379 3013 y Fj(2)1419 3062 y Fo(g)1466 3077 y Fj(1)1505 2981 y Fi(\000)1550 3062 y Fo(t)1585 3020 y Fn(\000)p Fj(1)1680 3062 y Fo(x)1735 2981 y Fi(\001)1781 3003 y Fj(2)1821 2981 y Fi(\000)1866 3062 y Fo(a)1917 3020 y Fj(1)1917 3086 y Fm(t)1957 3062 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h Fo(a)2350 3020 y Fj(2)2350 3086 y Fm(t)2390 3062 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2612 2981 y Fi(\001)2686 3062 y Fk(\024)28 b Fo(C)7 b(c)2910 3077 y Fm(t)2940 3062 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)386 3218 y Fp(from)29 b(whic)m(h)i(w)m(e)f (readily)g(get)g(the)f(lemma)i(b)m(y)f(the)g(F)-8 b(e\013erman-Phong)29 b(inequal-)386 3335 y(it)m(y)-8 b(.)2779 b Fe(\003)386 3508 y Fg(R)-5 b(emark)48 b Fp(4.3)p Fg(.)42 b Fp(W)-8 b(e)36 b(shall)g(not)f(use)i(Lemma)f(4.2.)52 b(Ho)m(w)m(ev)m(er)38 b(the)e(pro)s(of)e(will)i(b)s(e)386 3624 y(imp)s(ortan)m(t.)43 b(In)31 b(particular)f(w)m(e)i(shall)f(need)g(the)g(non-negativit)m(y)h (of)e(the)h(ab)s(o)m(v)m(e)386 3740 y(sym)m(b)s(ol)j Fo(c)762 3755 y Fm(t)791 3740 y Fp(.)486 3913 y(Let)k(for)g Fo(t;)17 b(\024)37 b Fk(\025)h Fp(1)f(and)i(0)e Fo(<)g Fp(2)p Fo(\016)k(<)c Fp(min)17 b(\()p Fo(\027)q(;)g Fp(2)p Fo(\016)2241 3877 y Fm(s)2277 3913 y Fp(\))38 b(with)h Fo(\027)44 b(<)37 b Fp(2)p Fo(=)p Fp(5)g(and)i Fo(\016)3213 3877 y Fm(s)3287 3913 y Fp(as)386 4030 y(in)33 b(\(2.14\))f(\(this)h(n) m(um)m(b)s(er)h(ma)m(y)g(b)s(e)f(tak)m(en)g(indep)s(enden)m(t)i(of)d Fo(E)39 b Fp(close)34 b(to)e Fo(E)3175 4045 y Fj(0)3215 4030 y Fp(,)g(cf.)386 4146 y(Remarks)i(2.2)e(\(1\)\),)469 4336 y Fo(b)510 4351 y Fm(t;\024)600 4336 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(F)1017 4351 y Fj(+)1076 4255 y Fi(\000)1122 4336 y Fo(\024)1178 4295 y Fn(\000)p Fj(1)1272 4336 y Fo(t)1307 4295 y Fj(2)p Fm(\016)1381 4336 y Fo(q)1428 4295 y Fm(s)1464 4336 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))1687 4255 y Fi(\001)1732 4336 y Fo(F)1795 4351 y Fn(\000)1855 4255 y Fi(\000)1900 4336 y Fo(t)1935 4295 y Fm(\027)1979 4336 y Fo(q)2026 4295 y Fn(\000)2084 4336 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2307 4255 y Fi(\001)1939 4503 y Fp(~)-52 b Fo(g)1983 4518 y Fj(1)2022 4422 y Fi(\000)2068 4503 y Fo(t)2103 4461 y Fn(\000)p Fj(1)2197 4503 y Fo(x)2252 4422 y Fi(\001)2302 4503 y Fp(~)f Fo(g)2345 4518 y Fj(2)2384 4503 y Fp(\()p Fo(\030)5 b Fp(\))27 b Fk(2)h Fo(S)2689 4518 y Fm(unif)2842 4422 y Fi(\000)2888 4503 y Fp(1)p Fo(;)17 b(g)3032 4455 y Fj(1)p Fn(\000)p Fm(\027;\027)3028 4525 y(t)3219 4422 y Fi(\001)3265 4503 y Fo(:)386 4676 y FC(Lemma)39 b(4.4.)j Fg(F)-7 b(or)34 b(al)5 b(l)34 b Fo(\017)28 b(>)g Fp(0)1278 4752 y Fi(\012)1325 4833 y Fo(b)1366 4792 y Fm(w)1366 4858 y(t;t)1436 4839 y Ff(\017)1471 4833 y Fp(\()p Fo(x;)17 b(p)p Fp(\))1695 4752 y Fi(\013)1742 4875 y Fm(t)1799 4833 y Fk(!)28 b Fp(0)34 b Fg(for)h Fo(t)28 b Fk(!)f(1)p Fo(:)691 b Fp(\(4.9\))386 5015 y Fg(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)33 b(shall)g(use)h(another)e(sc)m(heme)j(of)d(pro)s(of)g (from)g([D].)h(Let)1305 5171 y Fo(B)1379 5186 y Fm(t;\024)1497 5171 y Fp(=)27 b Fo(L)1666 5186 y Fj(1)1706 5171 y Fp(\()p Fo(t)p Fp(\))1817 5123 y Fn(\003)1856 5171 y Fo(b)1897 5130 y Fm(w)1897 5196 y(t;\024)1988 5171 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(L)2278 5186 y Fj(1)2318 5171 y Fp(\()p Fo(t)p Fp(\))p Fo(;)669 b Fp(\(4.10\))386 5333 y(cf.)44 b(\(4.5\),)32 b(and)g(write)i(for)e(an)m(y)h(\(large\))f Fo(t)1911 5348 y Fj(0)1128 5557 y Fk(h)p Fo(B)1241 5572 y Fm(t;\024)1331 5557 y Fk(i)1370 5589 y Fm(t)1427 5557 y Fp(=)c Fk(h)p Fo(B)1644 5572 y Fm(t)1669 5581 y Fh(0)1704 5572 y Fm(;\024)1768 5557 y Fk(i)1807 5589 y Fm(t)1832 5598 y Fh(0)1893 5557 y Fp(+)1991 5421 y Fi(Z)2091 5447 y Fm(t)2047 5647 y(t)2072 5656 y Fh(0)2137 5557 y Fk(h)p FC(D)p Fo(B)2336 5572 y Fm(s;\024)2433 5557 y Fk(i)2472 5589 y Fm(s)2508 5557 y Fo(ds:)493 b Fp(\(4.11\))p eop end %%Page: 22 22 TeXDict begin 22 21 bop 386 259 a Fl(22)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)486 459 y Fp(T)-8 b(o)37 b(sho)m(w)h(that)f(the)g(left)g(hand)g(side)i(of)d(\(4.11\))g(v)-5 b(anishes)39 b(as)e Fo(t)f Fk(!)f(1)h Fp(\(with)386 575 y Fo(\024)41 b Fp(=)g Fo(t)635 539 y Fm(\017)708 575 y Fp(\))f(w)m(e)h(lo)s(ok)f(at)g(the)h(in)m(tegrand)g(on)f(the)h(righ)m (t)f(hand)h(side:)60 b(As)41 b(in)f(the)386 691 y(pro)s(of)d(of)h (Lemma)h(4.1)f(w)m(e)i(ma)m(y)f(replace)g FC(D)g Fp(b)m(y)g FC(D)2335 706 y Fm(s)2410 691 y Fp(up)g(to)f(a)g(term)h Fo(r)3052 706 y Fm(s;\024)3187 691 y Fp(suc)m(h)386 807 y(that)686 876 y Fi(Z)785 902 y Fm(t)741 1101 y(t)766 1110 y Fh(0)832 1011 y Fo(r)876 1026 y Fm(s;\024)973 1011 y Fo(ds)27 b Fk(!)g Fp(0)32 b(uniformly)i(in)f Fo(\024)27 b Fk(\025)i Fp(1)j(and)h Fo(t)28 b Fk(\025)g Fo(t)2527 1026 y Fj(0)2599 1011 y Fp(as)33 b Fo(t)2754 1026 y Fj(0)2821 1011 y Fk(!)27 b(1)p Fo(:)486 1239 y Fp(Using)42 b(\(1.9\))e(and)h (Remark)g(4.3)g(w)m(e)g(ma)m(y)h(estimate)g(the)f(in)m(tegrand)g(up)g (to)386 1355 y(terms)33 b(of)g(this)g(t)m(yp)s(e)g(as)1174 1517 y Fk(\001)17 b(\001)g(\001)26 b(\024)1423 1436 y Fi(\012)1470 1517 y Fo(L)1536 1532 y Fj(1)1576 1517 y Fp(\()p Fo(s)p Fp(\))1698 1468 y Fn(\003)1737 1436 y Fi(\000)1783 1517 y Fo(b)1824 1476 y Fj(1)1824 1541 y Fm(s;\024)1922 1436 y Fi(\001)1967 1458 y Fm(w)2024 1517 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(L)2314 1532 y Fj(1)2354 1517 y Fp(\()p Fo(s)p Fp(\))2475 1436 y Fi(\013)2522 1558 y Fm(s)2559 1517 y Fo(;)386 1681 y Fp(where)564 1843 y Fo(b)605 1802 y Fj(1)605 1868 y Fm(s;\024)703 1843 y Fp(\()p Fo(x;)g(\030)5 b Fp(\))27 b(=)h Fo(\024)1113 1802 y Fn(\000)p Fj(1)1207 1843 y Fo(s)1253 1802 y Fj(2)p Fm(\016)1326 1762 y Fi(\000)1372 1843 y Fp(2)p Fo(\016)t(s)1514 1802 y Fn(\000)p Fj(1)1608 1843 y Fo(q)1655 1802 y Fm(s)1691 1843 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b(+)g Fk(f)p Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(;)17 b(q)2453 1802 y Fm(s)2490 1843 y Fp(\()p Fo(x;)g(\030)5 b Fp(\))o Fk(g)2762 1762 y Fi(\001)2808 1843 y Fo(c)2850 1858 y Fm(s;\024)2947 1843 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o(;)564 2007 y Fo(c)606 2022 y Fm(s;\024)703 2007 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(F)1134 1966 y Fn(0)1120 2031 y Fj(+)1179 1926 y Fi(\000)1225 2007 y Fo(\024)1281 1966 y Fn(\000)p Fj(1)1375 2007 y Fo(s)1421 1966 y Fj(2)p Fm(\016)1495 2007 y Fo(q)1542 1966 y Fm(s)1578 2007 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))1801 1926 y Fi(\001)1846 2007 y Fo(F)1909 2022 y Fn(\000)1968 1926 y Fi(\000)2014 2007 y Fo(s)2060 1966 y Fm(\027)2103 2007 y Fo(q)2150 1966 y Fn(\000)2209 2007 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2432 1926 y Fi(\001)2481 2007 y Fp(~)-53 b Fo(g)2524 2022 y Fj(1)2563 1926 y Fi(\000)2609 2007 y Fo(s)2655 1966 y Fn(\000)p Fj(1)2749 2007 y Fo(x)2804 1926 y Fi(\001)2854 2007 y Fp(~)g Fo(g)2897 2022 y Fj(2)2937 2007 y Fp(\()o Fo(\030)5 b Fp(\))p Fo(:)486 2174 y Fp(W)-8 b(e)44 b(compute,)j(cf.)78 b(\(2.14\),)46 b(that)d(for)h(all)f(large)h Fo(s)g Fp(and)g(a)f(large)h (constan)m(t)386 2290 y Fo(C)35 b(>)27 b Fp(0)801 2452 y Fk(\000)22 b Fo(C)7 b(s)1023 2411 y Fj(2)p Fm(\016)r Fn(\000)p Fm(\027)t Fn(\000)p Fj(1)1303 2452 y Fk(\000)22 b Fo(C)7 b(s)1525 2411 y Fj(2)p Fm(\016)r Fn(\000)p Fj(1)1688 2452 y Fo(q)1735 2411 y Fm(s)1772 2452 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(c)2036 2467 y Fm(s;\024)2133 2452 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))806 2616 y Fk(\024)28 b Fo(b)952 2574 y Fj(1)952 2640 y Fm(s;\024)1050 2616 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b Fk(\024)h Fo(C)7 b(s)1528 2574 y Fj(2)p Fm(\016)r Fn(\000)p Fm(\027)t Fn(\000)p Fj(1)1807 2616 y Fk(\000)23 b Fo(C)1984 2574 y Fn(\000)p Fj(1)2078 2616 y Fo(s)2124 2574 y Fj(2)p Fm(\016)r Fn(\000)p Fj(1)2288 2616 y Fo(q)2335 2574 y Fm(s)2371 2616 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(c)2636 2631 y Fm(s;\024)2733 2616 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(;)386 2778 y Fp(from)32 b(whic)m(h)i(w)m(e)g (conclude)g(that)1158 2981 y(lim)17 b(sup)1206 3061 y Fm(t)1231 3070 y Fh(0)1266 3061 y Fn(!1)1545 2981 y Fp(sup)1473 3062 y Fm(\024)p Fn(\025)p Fj(1)p Fm(;t)p Fn(\025)p Fm(t)1729 3071 y Fh(0)1781 2846 y Fi(Z)1880 2872 y Fm(t)1836 3071 y(t)1861 3080 y Fh(0)1926 2981 y Fk(h)p FC(D)p Fo(B)2125 2996 y Fm(s;\024)2222 2981 y Fk(i)2261 3013 y Fm(s)2298 2981 y Fo(ds)27 b Fk(\024)h Fp(0)p Fo(:)522 b Fp(\(4.12\))486 3213 y(As)36 b(for)g(the)g(\014rst)h(term)g(on)f(the)g(righ)m(t)h(hand) f(side)h(of)f(\(4.11\),)g(ob)m(viously)i(for)386 3329 y(\014xed)c Fo(t)657 3344 y Fj(0)1351 3450 y Fk(h)p Fo(B)1464 3465 y Fm(t)1489 3474 y Fh(0)1524 3465 y Fm(;\024)1588 3450 y Fk(i)1627 3482 y Fm(t)1652 3491 y Fh(0)1719 3450 y Fk(!)27 b Fp(0)h(for)k Fo(\024)c Fk(!)f(1)p Fo(:)715 b Fp(\(4.13\))486 3600 y(Com)m(bining)33 b(\(4.12\))f(and)h(\(4.13\))f (w)m(e)h(conclude)h(\(b)m(y)g(\014rst)f(\014xing)g Fo(t)2957 3615 y Fj(0)3029 3600 y Fp(\))g(that)1426 3761 y(lim)17 b(sup)1492 3840 y Fm(t)p Fn(!1)1839 3761 y Fk(h)p Fo(B)1952 3776 y Fm(t;t)2022 3757 y Ff(\017)2057 3761 y Fk(i)2096 3793 y Fm(t)2153 3761 y Fk(\024)28 b Fp(0)p Fo(;)386 3979 y Fp(whence)34 b(w)m(e)g(infer)f(\(4.9\).)1973 b Fe(\003)486 4151 y Fp(Next)36 b(w)m(e)g(\\absorb")f(the)h Fo(\017)f Fp(of)g(Lemma)h(4.4)f(in)m(to)g(the)h Fo(\016)j Fp(and)c(in)m(tro)s(duce)h(the)386 4267 y(sym)m(b)s(ols)511 4427 y Fo(b)552 4442 y Fm(t)582 4427 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(F)999 4442 y Fn(\000)1058 4347 y Fi(\000)1104 4427 y Fo(t)1139 4386 y Fj(2)p Fm(\016)1212 4427 y Fo(q)1259 4386 y Fm(s)1296 4427 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))1518 4347 y Fi(\001)1564 4427 y Fo(F)1627 4442 y Fn(\000)1686 4347 y Fi(\000)1732 4427 y Fo(t)1767 4386 y Fm(\027)1810 4427 y Fo(q)1857 4386 y Fn(\000)1916 4427 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2139 4347 y Fi(\001)2188 4427 y Fp(~)-53 b Fo(g)2231 4442 y Fj(1)2270 4347 y Fi(\000)2316 4427 y Fo(t)2351 4386 y Fn(\000)p Fj(1)2446 4427 y Fo(x)2501 4347 y Fi(\001)2550 4427 y Fp(~)h Fo(g)2594 4442 y Fj(2)2633 4427 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(;)511 4591 y(b)552 4550 y Fj(1)552 4615 y Fm(t)592 4591 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fk(\000)p Fo(t)1058 4550 y Fn(\000)p Fj(1)1153 4591 y Fo(F)1230 4550 y Fn(0)1216 4615 y(\000)1275 4510 y Fi(\000)1321 4591 y Fo(t)1356 4550 y Fj(2)p Fm(\016)1429 4591 y Fo(q)1476 4550 y Fm(s)1513 4591 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))1735 4510 y Fi(\001)1781 4591 y Fo(F)1844 4606 y Fn(\000)1903 4510 y Fi(\000)1949 4591 y Fo(t)1984 4550 y Fm(\027)2027 4591 y Fo(q)2074 4550 y Fn(\000)2133 4591 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2355 4510 y Fi(\001)2405 4591 y Fp(~)-53 b Fo(g)2448 4606 y Fj(1)2487 4510 y Fi(\000)2533 4591 y Fo(t)2568 4550 y Fn(\000)p Fj(1)2662 4591 y Fo(x)2717 4510 y Fi(\001)2767 4591 y Fp(~)g Fo(g)2810 4606 y Fj(2)2850 4591 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(;)3125 4509 y Fp(\(4.14\))386 4758 y(where)34 b(0)27 b Fo(<)h Fp(2)p Fo(\016)j(<)d Fp(min)17 b(\()p Fo(\027)q(;)g Fp(2)p Fo(\016)1481 4722 y Fm(s)1517 4758 y Fp(\))32 b(with)i Fo(\027)g(<)27 b Fp(2)p Fo(=)p Fp(5)32 b(and)h Fo(\016)2411 4722 y Fm(s)2480 4758 y Fp(as)g(in)g(\(2.14\).)42 b(Clearly)647 4952 y Fo(b)688 4967 y Fm(t)718 4952 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b Fk(2)g Fo(S)1123 4967 y Fm(unf)1252 4841 y Fi(\020)1311 4952 y Fp(1)p Fo(;)17 b(g)1455 4904 y Fj(1)p Fn(\000)p Fm(\027)1584 4881 y Fc(0)1605 4904 y Fm(;\027)1664 4881 y Fc(0)1451 4974 y Fm(t)1691 4841 y Fi(\021)1778 4952 y Fk(\022)28 b Fo(S)1943 4967 y Fm(unif)2096 4871 y Fi(\000)2142 4952 y Fp(1)p Fo(;)17 b(g)2286 4904 y Fj(1)p Fn(\000)p Fm(\027;\027)2282 4974 y(t)2473 4871 y Fi(\001)2518 4952 y Fp(;)114 b Fo(\027)2713 4910 y Fn(0)2765 4952 y Fp(=)27 b Fo(\027)i Fk(\000)23 b Fo(\016)n(:)486 5139 y Fp(W)-8 b(e)33 b(ha)m(v)m(e)g(the)g(follo)m (wing)g(in)m(tegral)g(estimate.)386 5316 y FC(Lemma)39 b(4.5.)j Fg(In)34 b(the)h(state)g Fo( )1585 5331 y Fj(1)1625 5316 y Fp(\()p Fo(t)p Fp(\))28 b(=)f Fo(L)1933 5331 y Fj(1)1973 5316 y Fp(\()p Fo(t)p Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))1297 5397 y Fi(Z)1397 5423 y Fn(1)1352 5623 y Fj(1)1488 5533 y Fk(j)1516 5452 y Fi(\012\000)1608 5533 y Fo(b)1649 5492 y Fj(1)1649 5557 y Fm(t)1689 5452 y Fi(\001)1735 5474 y Fm(w)1791 5533 y Fp(\()p Fo(x;)17 b(p)p Fp(\))2015 5452 y Fi(\013)2062 5572 y Fm(t)2092 5533 y Fk(j)p Fo(dt)27 b(<)h Fk(1)p Fo(:)661 b Fp(\(4.15\))p eop end %%Page: 23 23 TeXDict begin 23 22 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(23)386 459 y Fg(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)25 b(use)h(the)g(pro)s(ofs)e(of)g(Lemmas)i(4.2)f(and)g (4.4.)41 b(Notice)25 b(that)g(to)f(leading)386 575 y(order)33 b(\\the)f(deriv)-5 b(ativ)m(e")34 b(of)e(the)h(sym)m(b)s(ol)970 736 y Fo(F)1033 751 y Fj(+)1092 655 y Fi(\000)1138 736 y Fo(t)1173 695 y Fj(2)p Fm(\016)1247 736 y Fo(q)1294 695 y Fm(s)1330 736 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))1553 655 y Fi(\001)1598 736 y Fo(F)1661 751 y Fn(\000)1720 655 y Fi(\000)1766 736 y Fo(t)1801 695 y Fm(\027)1844 736 y Fo(q)1891 695 y Fn(\000)1950 736 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2173 655 y Fi(\001)2222 736 y Fp(~)-53 b Fo(g)2265 751 y Fj(1)2305 655 y Fi(\000)2350 736 y Fo(t)2385 695 y Fn(\000)p Fj(1)2480 736 y Fo(x)2535 655 y Fi(\001)2584 736 y Fp(~)h Fo(g)2628 751 y Fj(2)2667 736 y Fp(\()p Fo(\030)5 b Fp(\))386 897 y(is)33 b(indeed)h(non-p)s (ositiv)m(e,)g(and)e(that)h Fo(F)1849 861 y Fn(0)1835 921 y Fj(+)1922 897 y Fp(=)27 b Fk(\000)p Fo(F)2179 861 y Fn(0)2165 921 y(\000)2225 897 y Fp(.)1045 b Fe(\003)486 1068 y Fp(By)35 b(com)m(bining)h(Lemmas)g(4.1)e(and)h(4.4)f(w)m(e)i (conclude)g(the)f(follo)m(wing)g(lo)s(cal-)386 1184 y(ization)e (result.)386 1360 y FC(Prop)s(osition)43 b(4.6.)h Fg(F)-7 b(or)38 b(any)h(state)g Fo( )g Fp(=)c Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )43 b Fg(ob)-5 b(eying)47 b Fp(\(1.8\))38 b Fg(and)49 b Fp(\(1.9\))386 1477 y Fg(with)35 b Fo(f)j Fk(2)28 b Fo(C)855 1440 y Fn(1)848 1501 y Fj(0)930 1477 y Fp(\()p Fo(I)1011 1492 y Fj(0)1050 1477 y Fp(\))35 b Fg(wher)-5 b(e)34 b Fo(I)1441 1492 y Fj(0)1516 1477 y Fg(is)g(a)h(su\016ciently)g(smal)5 b(l)34 b(neighb)-5 b(orho)g(o)g(d)33 b(of)h Fo(E)3221 1492 y Fj(0)1069 1637 y Fk(jj)p Fo( )t Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)h Fo(b)1466 1596 y Fm(w)1466 1662 y(t)1523 1637 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)27 b(!)g Fp(0)35 b Fg(for)f Fo(t)28 b Fk(!)g(1)p Fo(:)433 b Fp(\(4.16\))486 1814 y(Using)38 b(the)g(sym)m(b)s(ol)h Fo(b)1318 1829 y Fm(t)1349 1814 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\))38 b(w)m(e)h(can)f(b)s(ound)g(p)s(o)m(w)m(ers)h(of)e Fo(\015)5 b Fp(,)40 b(cf.)59 b(\(2.17\).)g(If)386 1930 y(w)m(e)37 b(de\014ne)h Fo(\015)h Fp(=)34 b Fo(\015)5 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))36 b(as)h(in)f(\(2.3\))g(up)s(on)h (substituting)g Fo(E)43 b Fp(b)m(y)37 b(the)g(sym)m(b)s(ols)386 2047 y Fo(h)p Fp(\()p Fo(r)524 2062 y Fj(0)569 2047 y Fp(^)-55 b Fo(x)q(;)17 b(\030)5 b Fp(\))31 b(w)m(e)j(ma)m(y)f(consider) h(the)f(sym)m(b)s(ol)728 2216 y Fo(\015)784 2174 y Fm(\013)779 2240 y(t)833 2216 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(:=)f Fo(\015)1270 2174 y Fm(\013)1320 2216 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(b)1583 2231 y Fm(t)1613 2216 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\);)114 b Fo(\013)28 b Fk(2)g Fp(\()p FC(N)22 b Fk([)h(f)o Fp(0)p Fk(g)p Fp(\))2584 2167 y Fj(2)p Fm(n)p Fn(\000)p Fj(2)2756 2216 y Fo(:)342 b Fp(\(4.17\))486 2376 y(W)-8 b(e)33 b(ha)m(v)m(e)g(the)g(b)s(ounds) 1324 2537 y Fk(jj)p Fp(\()p Fo(\015)1474 2496 y Fm(\013)1469 2562 y(t)1523 2537 y Fp(\))1561 2489 y Fm(w)1618 2537 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fk(jj)27 b Fp(=)g Fo(O)2106 2457 y Fi(\000)2151 2537 y Fo(t)2186 2496 y Fn(\000)p Fm(\016)r Fn(j)p Fm(\013)p Fn(j)2364 2457 y Fi(\001)2409 2537 y Fo(:)689 b Fp(\(4.18\))1255 2746 y(5.)48 b(\000)38 b Fq(and)g(its)f(localiza)-7 b(tion)486 2920 y Fp(With)36 b(the)g(assumption)h(\(2.8\))f(w)m(e)h(de\014ne)g(op)s(erators)e Fo(G)h Fp(and)g(\000)g(as)g(follo)m(ws:)386 3037 y(The)d(righ)m(t)g (hand)g(side)h(of)e(\(2.18\))g(is)h(of)f(the)h(form)1320 3219 y Fo(\015)1376 3178 y Fj(\()p Fm(m)1465 3187 y Fh(0)1500 3178 y Fj(\))1560 3219 y Fp(=)27 b Fo(\015)1714 3234 y Fj(1)1775 3219 y Fp(+)1965 3125 y Fi(X)1873 3340 y Fj(2)p Fn(\024j)p Fm(\013)p Fn(j\024)p Fm(m)2165 3349 y Fh(0)2217 3219 y Fo(c)2259 3234 y Fm(\013)2308 3219 y Fo(\015)2364 3178 y Fm(\013)2414 3219 y Fo(;)386 3495 y Fp(here)j Fo(c)636 3510 y Fm(\013)715 3495 y Fp(and)g Fo(\015)958 3458 y Fm(\013)1037 3495 y Fp(dep)s(end)h(smo)s(othly)f(of) g Fo(E)6 b Fp(.)42 b(As)30 b(done)g(in)g(\(4.17\))f(w)m(e)i(substitute) 1595 3655 y Fo(E)i Fp(=)28 b Fo(h)p Fp(\()p Fo(r)1942 3670 y Fj(0)1987 3655 y Fp(^)-55 b Fo(x)q(;)17 b(\030)5 b Fp(\))1007 b(\(5.1\))386 3823 y(and)36 b(m)m(ultiply)i(suitably)g(b)m (y)f(the)g(factors)1985 3799 y(~)1985 3823 y(~)-53 b Fo(g)2028 3838 y Fj(1)2067 3823 y Fp(\()p Fo(t)2140 3786 y Fn(\000)p Fj(1)2235 3823 y Fo(x)p Fp(\))33 b(and)2554 3799 y(~)2554 3823 y(~)-53 b Fo(g)2597 3838 y Fj(1)2636 3823 y Fp(\()p Fo(\030)5 b Fp(\))36 b(as)g(in)m(tro)s(duced)386 3939 y(in)i(Section)h(3)e(\(with)i(small)f(supp)s(orts\).)60 b(Precisely)40 b(w)m(e)f(pic)m(k)h Fo(l)e Fk(\024)f Fo(n)26 b Fk(\000)h Fp(1)37 b(suc)m(h)386 4055 y(that)32 b(\(2.8\))g(holds)i (and)e(write)578 4216 y Fo(\015)629 4231 y Fj(1)696 4216 y Fp(=)c Fo(c)842 4231 y Fm(l)868 4216 y Fp(\()p Fo(\030)e Fk(\000)d Fo(\030)5 b Fp(\()o Fo(E)1232 4231 y Fj(0)1272 4216 y Fp(\)\))22 b Fk(\001)g Fo(!)1481 4231 y Fm(l)1506 4216 y Fp(\()p Fo(E)1616 4231 y Fj(0)1656 4216 y Fp(\))g(+)g Fo(r)1858 4231 y Fm(E)1918 4216 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o(;)114 b Fo(c)2323 4231 y Fm(l)2377 4216 y Fp(=)28 b Fo(@)2532 4231 y Fm(\027)2567 4243 y Ff(l)2595 4216 y Fo(\015)2646 4231 y Fj(1)2685 4216 y Fp(\()p Fo(w)s(;)17 b(E)2912 4231 y Fj(0)2951 4216 y Fp(\))2989 4245 y Fn(j)p Fm(w)r Fj(=0)3155 4216 y Fo(:)386 4389 y Fp(Then)34 b(w)m(e)f(de\014ne) h(the)f(op)s(erator)f Fo(G)c Fp(=)f Fo(G)1912 4404 y Fm(t)1969 4389 y Fp(=)h Fo(\015)2129 4353 y Fm(w)2124 4414 y(t)2186 4389 y Fp(\()o Fo(x;)17 b(p)p Fp(\))33 b(b)m(y)h(the)f(sym)m(b)s(ol)445 4551 y Fo(\015)496 4566 y Fm(t)526 4551 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(\015)935 4510 y Fj(1)975 4551 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h Fo(\015)1373 4510 y Fj(2)1368 4576 y Fm(t)1413 4551 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o(;)445 4711 y Fo(\015)501 4670 y Fj(1)541 4711 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g(\()p Fo(\030)g Fk(\000)c Fo(\030)5 b Fp(\()o Fo(E)1259 4726 y Fj(0)1299 4711 y Fp(\)\))22 b Fk(\001)f Fo(!)1507 4726 y Fm(l)1533 4711 y Fp(\()p Fo(E)1643 4726 y Fj(0)1683 4711 y Fp(\))p Fo(;)445 4992 y(\015)501 4951 y Fj(2)496 5017 y Fm(t)541 4992 y Fp(\()p Fo(x;)c(\030)5 b Fp(\))27 b(=)g(\()p Fo(c)974 5007 y Fm(l)1000 4992 y Fp(\))1038 4944 y Fn(\000)p Fj(1)1133 4792 y Fi(0)1133 4971 y(@)1220 4992 y Fo(r)1264 5007 y Fm(E)1323 4992 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b(+)1757 4897 y Fi(X)1666 5113 y Fj(2)p Fn(\024j)p Fm(\013)p Fn(j\024)p Fm(m)1958 5122 y Fh(0)2009 4992 y Fo(c)2051 5007 y Fm(\013)2101 4992 y Fo(\015)2157 4951 y Fm(\013)2206 4992 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2429 4792 y Fi(1)2429 4971 y(A)2519 4969 y Fp(~)2519 4992 y(~)-52 b Fo(g)2563 5007 y Fj(1)2602 4911 y Fi(\000)2648 4992 y Fo(t)2683 4951 y Fn(\000)p Fj(1)2777 4992 y Fo(x)2832 4911 y Fi(\001)2882 4969 y Fp(~)2882 4992 y(~)f Fo(g)2925 5007 y Fj(2)2964 4992 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(:)3174 4831 y Fp(\(5.2\))386 5274 y(F)-8 b(or)45 b(the)i(second)h(term)e(the)h (substitution)h(\(5.1\))e(is)g(used.)86 b(Let)46 b(\000)51 b(=)g(\000)3218 5289 y Fm(t)3299 5274 y Fp(=)386 5390 y(Re)17 b(\()p Fo(G)p Fp(\))o(.)486 5506 y(Clearly)39 b(the)f(quan)m(tization)i(of)d(this)i(second)h(term)e Fo(B)2518 5521 y Fj(1)2558 5506 y Fp(\()p Fo(t)p Fp(\))f(=)g(\()p Fo(\015)2913 5470 y Fj(2)2908 5531 y Fm(t)2953 5506 y Fp(\))2990 5454 y Fm(w)3047 5506 y Fp(\()p Fo(x;)17 b(p)p Fp(\))38 b(is)386 5623 y(b)s(ounded.)p eop end %%Page: 24 24 TeXDict begin 24 23 bop 386 259 a Fl(24)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)486 459 y Fp(W)-8 b(e)33 b(shall)g(assume)h(that)1568 637 y Fo(\016)t Fp(\()p Fo(m)1738 652 y Fj(0)1799 637 y Fp(+)23 b(1\))k Fk(\025)h Fp(1)p Fo(;)981 b Fp(\(5.3\))386 816 y(where)34 b Fo(\016)d(<)d Fp(2)895 780 y Fn(\000)p Fj(1)1006 816 y Fp(min)17 b(\()p Fo(\027)q(;)g Fp(2)p Fo(\016)1408 831 y Fm(s)1444 816 y Fp(\))33 b(is)g(giv)m(en)h(as)e(in)h(Prop)s(osition)g(4.6.)486 932 y(W)-8 b(e)33 b(shall)g(use)h(the)g(op)s(erator)e Fo(L)1679 947 y Fj(1)1719 932 y Fp(\()p Fo(t)p Fp(\))h(giv)m(en)h(in)f (\(4.5\).)45 b(Let)33 b(us)g(in)m(tro)s(duce)h(the)386 1048 y(notation)42 b Fo(L)852 1063 y Fj(2)892 1048 y Fp(\()p Fo(t)p Fp(\))i(=)h Fo(b)1209 1012 y Fm(w)1209 1073 y(t)1266 1048 y Fp(\()p Fo(x;)17 b(p)p Fp(\))42 b(for)g(the)h(quan)m(tization)h(of)e(the)g(\014rst)h(sym)m(b)s(ol)h(of) 386 1164 y(\(4.14\).)f(Let)32 b(us)i(also)e(in)m(tro)s(duce)i(the)f (\\bigger")f(lo)s(calization)h(op)s(erator)601 1377 y Fo(L)667 1392 y Fj(3)707 1377 y Fp(\()p Fo(t)p Fp(\))28 b(=)949 1266 y Fi(\020)1005 1351 y Fp(~)1009 1377 y Fo(b)1050 1392 y Fm(t)1080 1266 y Fi(\021)1140 1289 y Fm(w)1196 1377 y Fp(\()p Fo(x;)17 b(p)p Fp(\);)598 1545 y(~)601 1571 y Fo(b)642 1586 y Fm(t)672 1571 y Fp(\()p Fo(x;)g(\030)5 b Fp(\))27 b(=)h Fo(F)1089 1586 y Fn(\000)1148 1491 y Fi(\000)1194 1571 y Fp(2)1243 1530 y Fn(\000)p Fj(1)1337 1571 y Fo(t)1372 1530 y Fj(2)p Fm(\016)1445 1571 y Fo(q)1492 1530 y Fm(s)1529 1571 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))1751 1491 y Fi(\001)1797 1571 y Fo(F)1860 1586 y Fn(\000)1919 1491 y Fi(\000)1965 1571 y Fp(2)2014 1530 y Fn(\000)p Fj(1)2108 1571 y Fo(t)2143 1530 y Fm(\027)2186 1571 y Fo(q)2233 1530 y Fn(\000)2292 1571 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2515 1491 y Fi(\001)2564 1571 y Fp(~)-53 b Fo(g)2607 1586 y Fj(1)2647 1491 y Fi(\000)2692 1571 y Fo(t)2727 1530 y Fn(\000)p Fj(1)2822 1571 y Fo(x)2877 1491 y Fi(\001)2926 1571 y Fp(~)h Fo(g)2970 1586 y Fj(2)3009 1571 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(:)386 1750 y Fp(Notice)33 b(that)f(also)1016 1909 y(~)1019 1935 y Fo(b)1060 1950 y Fm(t)1090 1935 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b Fk(2)g Fo(S)1495 1950 y Fm(unif)1648 1825 y Fi(\020)1707 1935 y Fp(1)p Fo(;)17 b(g)1851 1888 y Fj(1)p Fn(\000)p Fm(\027)1980 1865 y Fc(0)2002 1888 y Fm(;\027)2061 1865 y Fc(0)1847 1958 y Fm(t)2087 1825 y Fi(\021)2146 1935 y Fp(;)114 b Fo(\027)2341 1894 y Fn(0)2393 1935 y Fp(=)27 b Fo(\027)i Fk(\000)23 b Fo(\016)n(;)386 2140 y Fp(and)33 b(that)f(indeed)i(for)e(example)1185 2318 y(\()p Fo(I)e Fk(\000)22 b Fo(L)1461 2333 y Fj(3)1501 2318 y Fp(\()p Fo(t)p Fp(\)\))p Fo(L)1716 2333 y Fj(2)1756 2318 y Fp(\()p Fo(t)p Fp(\))p Fo(L)1933 2333 y Fj(1)1973 2318 y Fp(\()p Fo(t)p Fp(\))28 b(=)f Fo(O)2293 2238 y Fi(\000)2338 2318 y Fo(t)2373 2277 y Fn(\0001)2503 2238 y Fi(\001)2549 2318 y Fo(:)598 b Fp(\(5.4\))486 2499 y(W)-8 b(e)33 b(obtain)f(from)g (\(2.17\),)g(\(5.3\))g(and)h(b)s(ounds)g(lik)m(e)h(\(4.18\))e(that)1093 2679 y Fo(L)1159 2694 y Fj(3)1199 2679 y Fo(i)p Fp([)p Fo(H)r(;)17 b(G)p Fp(])p Fo(L)1556 2694 y Fj(3)1623 2679 y Fp(=)28 b Fk(\000)p Fo(L)1870 2694 y Fj(3)1912 2660 y Fp(~)1910 2679 y Fo(t)1945 2638 y Fn(\000)p Fj(1)2040 2679 y Fo(GL)2183 2694 y Fj(3)2245 2679 y Fp(+)22 b Fo(O)2421 2598 y Fi(\000)2466 2679 y Fo(t)2501 2638 y Fn(\000)p Fj(2)2595 2598 y Fi(\001)2641 2679 y Fo(;)506 b Fp(\(5.5\))386 2869 y(where)34 b Fo(t)e Fp(is)h(omitted)g(in)g(the)g(notation)f(and) 2059 2850 y(~)2058 2869 y Fo(t)2093 2833 y Fn(\000)p Fj(1)2220 2869 y Fp(is)h(the)g(W)-8 b(eyl)34 b(quan)m(tization)f(of)386 2985 y(the)g(sym)m(b)s(ol)1033 3217 y Fk(\000)1205 3150 y Fo(@)1256 3165 y Fm(\026)1303 3150 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p 1120 3194 547 4 v 1120 3286 a Fo(x)23 b Fk(\001)f Fo(!)t Fp(\()o Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))1677 3217 y Fo(\014)1738 3176 y Fm(s)1732 3242 y Fj(1)1774 3217 y Fp(\()p Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))2132 3194 y(~)2132 3217 y(~)-52 b Fo(g)2176 3232 y Fj(1)2215 3136 y Fi(\000)2260 3217 y Fo(t)2295 3176 y Fn(\000)p Fj(1)2390 3217 y Fo(x)2445 3136 y Fi(\001)2494 3194 y Fp(~)2494 3217 y(~)g Fo(g)2538 3232 y Fj(2)2577 3217 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(:)486 3470 y Fp(W)-8 b(e)33 b(ma)m(y)g(assume)h(that)e(the)h(supp)s(orts)h (of)2095 3447 y(~)2095 3470 y(~)-52 b Fo(g)2139 3485 y Fj(1)2210 3470 y Fp(and)2404 3447 y(~)2404 3470 y(~)f Fo(g)2447 3485 y Fj(1)2519 3470 y Fp(are)32 b(so)h(small)g(that)944 3650 y(Re)1075 3569 y Fi(\000)1122 3631 y Fp(~)1121 3650 y Fo(t)1156 3609 y Fn(\000)p Fj(1)1251 3569 y Fi(\001)1324 3650 y Fk(\025)28 b Fo(t)1464 3609 y Fn(\000)p Fj(1)1575 3650 y Fp(Re)1707 3569 y Fi(\000)1756 3626 y Fp(~)1756 3650 y(~)-52 b Fo(g)1800 3665 y Fj(1)1839 3569 y Fi(\000)1884 3650 y Fo(t)1919 3609 y Fn(\000)p Fj(1)2014 3650 y Fo(x)2069 3569 y Fi(\001)2119 3626 y Fp(~)2119 3650 y(~)f Fo(g)2162 3665 y Fj(2)2201 3650 y Fp(\()p Fo(p)p Fp(\))2326 3569 y Fi(\001)2394 3650 y Fp(+)22 b Fo(O)2570 3569 y Fi(\000)2615 3650 y Fo(t)2650 3609 y Fn(\000)p Fj(2)2744 3569 y Fi(\001)2790 3650 y Fo(:)357 b Fp(\(5.6\))486 3828 y(W)-8 b(e)33 b(ha)m(v)m(e)g(the) g(follo)m(wing)g(lo)s(calization)g(result.)386 4015 y FC(Prop)s(osition)45 b(5.1.)h Fg(L)-5 b(et)41 b Fo( )t(;)17 b(\027)47 b Fg(and)41 b Fo(\016)k Fg(b)-5 b(e)41 b(given)f(as)h(in)f (Pr)-5 b(op)g(osition)41 b(4.6)f(and)386 4131 y(supp)-5 b(ose)47 b(\(5.3\).)82 b(Then)46 b(for)i(al)5 b(l)47 b Fo(\033)55 b Fk(2)c Fp(\()p Fo(\027)1983 4095 y Fn(0)2007 4131 y Fo(;)17 b Fp(1)22 b Fk(\000)g Fo(\027)2275 4095 y Fn(0)2299 4131 y Fp(\))p Fg(,)51 b Fo(\027)2472 4095 y Fn(0)2546 4131 y Fp(=)g Fo(\027)38 b Fk(\000)32 b Fo(\016)t Fg(,)51 b(and)c(with)386 4247 y Fo(P)41 b Fp(=)28 b Fo(P)657 4262 y Fm(t)714 4247 y Fp(=)f Fo(GG)971 4211 y Fn(\003)1033 4247 y Fp(+)22 b Fo(G)1208 4211 y Fn(\003)1247 4247 y Fo(G)35 b Fg(wher)-5 b(e)34 b Fo(G)28 b Fp(=)f Fo(G)1919 4262 y Fm(t)1984 4247 y Fg(is)34 b(given)g(as)h(ab)-5 b(ove)1132 4341 y Fi(\015)1132 4401 y(\015)1187 4426 y Fo(F)1250 4441 y Fj(+)1309 4345 y Fi(\000)1355 4426 y Fo(t)1390 4385 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1562 4426 y Fo(P)1639 4345 y Fi(\001)1684 4426 y Fo( )t Fp(\()p Fo(t)p Fp(\))1862 4341 y Fi(\015)1862 4401 y(\015)1946 4426 y Fk(!)27 b Fp(0)34 b Fg(for)h Fo(t)28 b Fk(!)f(1)p Fo(:)545 b Fp(\(5.7\))386 4614 y Fg(Pr)-5 b(o)g(of.)41 b Fp(Using)33 b(the)g(calculus)h(w)m(e)g(compute)g(\(with)f(some)g (patience\))507 4793 y Fo(L)573 4808 y Fj(3)612 4793 y Fo(i)p Fp([)q Fo(H)r(;)17 b(P)d Fp(])o Fo(L)969 4808 y Fj(3)1037 4793 y Fp(=)27 b(2)17 b(Re)f(\()p Fo(L)1441 4808 y Fj(3)1481 4793 y Fo(i)p Fp([)p Fo(H)r(;)h(G)p Fp(])p Fo(L)1838 4808 y Fj(3)1878 4793 y Fo(G)1955 4752 y Fn(\003)2016 4793 y Fp(+)23 b Fo(G)2192 4752 y Fn(\003)2231 4793 y Fo(L)2297 4808 y Fj(3)2337 4793 y Fo(i)p Fp([)p Fo(H)r(;)17 b(G)p Fp(])p Fo(L)2694 4808 y Fj(3)2734 4793 y Fp(\))724 4944 y(+)22 b(Re)17 b(\()o Fo(L)1057 4959 y Fj(3)1097 4944 y Fo(i)p Fp([)q Fo(H)r(;)g(G)p Fp(][)p Fo(G)1493 4903 y Fn(\003)1532 4944 y Fo(;)g(L)1642 4959 y Fj(3)1681 4944 y Fp(])23 b Fk(\000)f Fp([)p Fo(G)1934 4903 y Fn(\003)1974 4944 y Fo(;)17 b(L)2084 4959 y Fj(3)2123 4944 y Fp(])p Fo(i)p Fp([)q Fo(H)r(;)g(G)p Fp(])p Fo(L)2508 4959 y Fj(3)2547 4944 y Fp(\))724 5095 y(+)22 b(Re)17 b(\()o Fo(L)1057 5110 y Fj(3)1097 5095 y Fo(i)p Fp([)q Fo(H)r(;)g(G)1362 5054 y Fn(\003)1401 5095 y Fp(][)p Fo(G;)g(L)1642 5110 y Fj(3)1681 5095 y Fp(])23 b Fk(\000)f Fp([)p Fo(G;)17 b(L)2044 5110 y Fj(3)2084 5095 y Fp(])p Fo(i)p Fp([)p Fo(H)r(;)g(G)2375 5054 y Fn(\003)2415 5095 y Fp(])p Fo(L)2508 5110 y Fj(3)2547 5095 y Fp(\))534 5264 y(=)28 b(2)17 b(Re)f(\()p Fo(L)939 5279 y Fj(3)979 5264 y Fo(i)p Fp([)p Fo(H)r(;)h(G)p Fp(])p Fo(L)1336 5279 y Fj(3)1376 5264 y Fo(G)1453 5223 y Fn(\003)1514 5264 y Fp(+)22 b Fo(G)1689 5223 y Fn(\003)1729 5264 y Fo(L)1795 5279 y Fj(3)1834 5264 y Fo(i)p Fp([)q Fo(H)r(;)17 b(G)p Fp(])p Fo(L)2192 5279 y Fj(3)2231 5264 y Fp(\))22 b(+)g Fo(c)2431 5223 y Fm(w)2431 5288 y(t)2488 5264 y Fp(\()p Fo(x;)17 b(p)p Fp(\))22 b(+)g Fo(O)2910 5183 y Fi(\000)2955 5264 y Fo(t)2990 5223 y Fj(2)p Fm(\027)3064 5199 y Fc(0)3087 5223 y Fn(\000)p Fj(3)3181 5183 y Fi(\001)3227 5264 y Fo(;)386 5442 y Fp(where)510 5621 y Fo(c)552 5636 y Fm(t)581 5621 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(c)977 5636 y Fm(t)1034 5621 y Fp(=)g(2)17 b(Re)1335 5540 y Fi(\000\010)1435 5595 y Fp(~)1439 5621 y Fo(b)1480 5636 y Fm(t)1510 5621 y Fo(;)1554 5540 y Fi(\010)1608 5595 y Fp(~)1612 5621 y Fo(b)1653 5636 y Fm(t)1683 5621 y Fo(;)p 1727 5543 81 4 v 21 w Fp(~)-53 b Fo(\015)1778 5636 y Fm(t)1807 5540 y Fi(\011\011)1923 5621 y Fk(f)p Fo(h;)20 b Fp(~)-52 b Fo(\015)2124 5636 y Fm(t)2153 5621 y Fk(g)2219 5540 y Fi(\001)2292 5621 y Fk(2)29 b Fo(S)2447 5636 y Fm(unf)2576 5540 y Fi(\000)2621 5621 y Fo(t)2656 5580 y Fj(3)p Fm(\027)2730 5556 y Fc(0)2753 5580 y Fn(\000)p Fj(3)2848 5621 y Fo(;)17 b(g)2943 5574 y Fj(1)p Fn(\000)p Fm(\027)3072 5550 y Fc(0)3093 5574 y Fm(;\027)3152 5550 y Fc(0)2939 5644 y Fm(t)3178 5540 y Fi(\001)3224 5621 y Fo(:)p eop end %%Page: 25 25 TeXDict begin 25 24 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(25)386 459 y Fp(Applying)35 b(\(5.5\))e(to)h(the)g (\014rst)g(t)m(w)m(o)h(terms)g(on)f(the)g(righ)m(t)g(hand)g(side)h(and) f(sym-)386 575 y(metrizing)f(yields)469 785 y Fo(L)535 800 y Fj(3)575 785 y Fo(i)p Fp([)p Fo(H)r(;)17 b(P)d Fp(])o Fo(L)931 800 y Fj(3)999 785 y Fp(=)27 b Fk(\000)p Fo(L)1245 800 y Fj(3)1286 704 y Fi(\010)1344 785 y Fo(P)j Fp(Re)1569 704 y Fi(\000)1616 766 y Fp(~)1614 785 y Fo(t)1649 744 y Fn(\000)p Fj(1)1744 704 y Fi(\001)1812 785 y Fp(+)22 b Fo(h:c:)2062 704 y Fi(\011)2120 785 y Fo(L)2186 800 y Fj(3)1291 976 y Fp(+)g(Re)1520 895 y Fi(\000)1566 976 y Fo(GO)1721 895 y Fi(\000)1766 976 y Fo(t)1801 935 y Fn(\000)p Fj(2)1895 895 y Fi(\001)1963 976 y Fp(+)g Fo(G)2138 935 y Fn(\003)2178 976 y Fo(O)2256 895 y Fi(\000)2301 976 y Fo(t)2336 935 y Fn(\000)p Fj(2)2430 895 y Fi(\001\001)2544 976 y Fp(+)g Fo(O)2720 865 y Fi(\020)2778 976 y Fo(t)2813 935 y Fj(2)p Fm(\027)2887 911 y Fc(0)2910 935 y Fn(\000)p Fj(3)3005 865 y Fi(\021)3064 976 y Fo(:)83 b Fp(\(5.8\))386 1188 y(Notice)33 b(that)f(the)h(con)m(tribution)h(from)e Fo(c)1899 1152 y Fm(w)1899 1213 y(t)1956 1188 y Fp(\()p Fo(x;)17 b(p)p Fp(\))32 b(disapp)s(ears)i(and)f(that)f(w)m(e)i(use)461 1371 y Fo(P)c Fp(Re)686 1290 y Fi(\000)733 1352 y Fp(~)732 1371 y Fo(t)767 1330 y Fn(\000)p Fj(1)861 1290 y Fi(\001)929 1371 y Fp(+)22 b Fo(h:c:)28 b Fp(=)g(2)p Fo(G)17 b Fp(Re)1585 1290 y Fi(\000)1632 1352 y Fp(~)1630 1371 y Fo(t)1665 1330 y Fn(\000)p Fj(1)1760 1290 y Fi(\001)1806 1371 y Fo(G)1883 1330 y Fn(\003)1944 1371 y Fp(+)22 b(2)p Fo(G)2168 1330 y Fn(\003)2224 1371 y Fp(Re)2356 1290 y Fi(\000)2403 1352 y Fp(~)2401 1371 y Fo(t)2436 1330 y Fn(\000)p Fj(1)2531 1290 y Fi(\001)2577 1371 y Fo(G)g Fp(+)g Fo(O)2852 1290 y Fi(\000)2897 1371 y Fo(t)2932 1330 y Fn(\000)p Fj(3)3026 1290 y Fi(\001)3072 1371 y Fo(:)75 b Fp(\(5.9\))486 1551 y(W)-8 b(e)35 b(shall)h(use)g(the)g(sc)m(heme)i(of)c(the)i(pro)s(of)e (of)h(Lemma)h(4.4.)51 b(Consider)37 b(with)386 1668 y Fo(\024)28 b Fp(=)f Fo(t)608 1632 y Fm(\017)674 1668 y Fp(for)32 b(a)g(small)h Fo(\017)28 b(>)g Fp(0)k(the)h(observ)-5 b(able)643 1849 y Fo(A)p Fp(\()p Fo(t;)17 b(\024)p Fp(\))28 b(=)f Fo(L)1124 1864 y Fj(1)1164 1849 y Fp(\()p Fo(t)p Fp(\))1275 1800 y Fn(\003)1315 1849 y Fo(F)1378 1864 y Fj(+)1437 1849 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fo(L)1769 1864 y Fj(2)1809 1849 y Fp(\()p Fo(t)p Fp(\))1920 1800 y Fj(2)1959 1849 y Fo(F)2022 1864 y Fj(+)2082 1849 y Fp(\()o Fo(B)g Fp(\()q Fo(t)p Fp(\)\))p Fo(L)2414 1864 y Fj(1)2453 1849 y Fp(\()p Fo(t)p Fp(\))q(;)643 2009 y Fo(B)g Fp(\()p Fo(t)p Fp(\))28 b(=)g Fo(B)5 b Fp(\()p Fo(t)p Fp(;)17 b Fo(\024)p Fp(\))27 b(=)1408 1984 y(\026)1386 2009 y Fo(G)1485 1984 y Fp(\026)1463 2009 y Fo(G)1540 1968 y Fn(\003)1601 2009 y Fp(+)1722 1984 y(\026)1699 2009 y Fo(G)1776 1968 y Fn(\003)1838 1984 y Fp(\026)1816 2009 y Fo(G;)2056 1984 y Fp(\026)2034 2009 y Fo(G)g Fp(=)2264 1984 y(\026)2242 2009 y Fo(G)p Fp(\()p Fo(t)p Fp(;)17 b Fo(\024)p Fp(\))28 b(=)f Fo(\024)2717 1968 y Fn(\000)p Fj(1)2812 2009 y Fo(t)2847 1968 y Fj(1)p Fn(\000)p Fm(\033)2984 2009 y Fo(G)3061 2024 y Fm(t)3090 2009 y Fo(:)486 2190 y Fp(As)j(b)s(efore)h(w)m(e)g(\014rst)g(compute)g(the)g(Heisen)m(b)s (erg)h(deriv)-5 b(ativ)m(e)32 b(treating)e Fo(\024)g Fp(as)h(a)386 2306 y(parameter)i(and)g(split)g(\(with)g Fo(L)1585 2321 y Fm(j)1650 2306 y Fp(=)27 b Fo(L)1819 2321 y Fm(j)1856 2306 y Fp(\()p Fo(t)p Fp(\)\))989 2487 y FC(D)p Fo(A)p Fp(\()p Fo(t;)17 b(\024)p Fp(\))27 b(=)h Fo(T)1547 2502 y Fj(1)1587 2487 y Fp(\()o Fo(t;)17 b(\024)p Fp(\))23 b(+)f Fo(T)1975 2502 y Fj(2)2014 2487 y Fp(\()p Fo(t;)17 b(\024)p Fp(\))22 b(+)g Fo(T)2402 2502 y Fj(3)2442 2487 y Fp(\()p Fo(t;)17 b(\024)p Fp(\);)989 2647 y Fo(T)1046 2662 y Fj(1)1113 2647 y Fp(=)28 b Fo(L)1283 2606 y Fn(\003)1283 2672 y Fj(1)1322 2647 y Fo(F)1385 2662 y Fj(+)1445 2647 y Fp(\()o Fo(B)5 b Fp(\()q Fo(t)p Fp(\)\))p Fo(L)1777 2606 y Fj(2)1777 2672 y(2)1816 2647 y Fp(\()p FC(D)p Fo(F)2003 2662 y Fj(+)2062 2647 y Fp(\()p Fo(B)g Fp(\()p Fo(t)p Fp(\))q(\)\))p Fo(L)2433 2662 y Fj(1)2494 2647 y Fp(+)22 b Fo(h:c:;)989 2808 y(T)1046 2823 y Fj(2)1113 2808 y Fp(=)28 b Fo(L)1283 2767 y Fn(\003)1283 2833 y Fj(1)1322 2808 y Fo(F)1385 2823 y Fj(+)1445 2808 y Fp(\()o Fo(B)5 b Fp(\()q Fo(t)p Fp(\)\))1711 2728 y Fi(\000)1756 2808 y FC(D)p Fo(L)1908 2767 y Fj(2)1908 2833 y(2)1948 2728 y Fi(\001)1994 2808 y Fo(L)2060 2823 y Fj(2)2099 2808 y Fo(F)2162 2823 y Fj(+)2222 2808 y Fp(\()p Fo(B)g Fp(\()p Fo(t)p Fp(\)\))p Fo(L)2554 2823 y Fj(1)2594 2808 y Fo(;)989 2969 y(T)1046 2984 y Fj(3)1113 2969 y Fp(=)28 b Fo(L)1283 2928 y Fn(\003)1283 2993 y Fj(1)1322 2969 y Fo(F)1385 2984 y Fj(+)1445 2969 y Fp(\()o Fo(B)5 b Fp(\()q Fo(t)p Fp(\)\))p Fo(L)1777 2928 y Fj(2)1777 2993 y(2)1816 2969 y Fo(F)1879 2984 y Fj(+)1939 2969 y Fp(\()p Fo(B)g Fp(\()p Fo(t)p Fp(\)\))p FC(D)p Fo(L)2357 2984 y Fj(1)2419 2969 y Fp(+)22 b Fo(h:c:)486 3155 y Fp(The)33 b(analogue)g(of)f(\(4.11\))f(is)537 3403 y Fk(h)p Fo(A)p Fp(\()p Fo(t;)17 b(\024)p Fp(\))p Fk(i)898 3432 y Fm(t)956 3403 y Fp(=)27 b Fk(h)p Fo(A)p Fp(\()p Fo(t)1244 3418 y Fj(0)1284 3403 y Fo(;)17 b(\024)p Fp(\))p Fk(i)1460 3432 y Fm(t)1485 3441 y Fh(0)1547 3403 y Fp(+)1645 3268 y Fi(Z)1744 3294 y Fm(t)1700 3493 y(t)1725 3502 y Fh(0)1791 3403 y Fk(h)o Fo(T)1886 3418 y Fj(1)1926 3403 y Fp(\()p Fo(s;)g(\024)p Fp(\))22 b(+)g Fo(T)2325 3418 y Fj(2)2364 3403 y Fp(\()p Fo(s;)17 b(\024)p Fp(\))22 b(+)g Fo(T)2763 3418 y Fj(3)2803 3403 y Fp(\()p Fo(s;)17 b(\024)p Fp(\))o Fk(i)3063 3432 y Fm(s)3100 3403 y Fo(ds:)3125 3586 y Fp(\(5.10\))486 3702 y(W)-8 b(e)33 b(shall)g(pro)m(v)m(e)h(that)935 3944 y(lim)17 b(sup)984 4023 y Fm(t)1009 4032 y Fh(0)1044 4023 y Fn(!1)1250 3944 y Fp(sup)1254 4025 y Fm(t)p Fn(\025)p Fm(t)1359 4034 y Fh(0)1414 3809 y Fi(Z)1513 3835 y Fm(t)1469 4034 y(t)1494 4043 y Fh(0)1560 3944 y Fk(h)o Fo(T)1655 3959 y Fm(i)1684 3944 y Fp(\()p Fo(s;)g(\024)p Fp(\))o Fk(i)1944 3973 y Fm(s)1981 3944 y Fo(ds)27 b Fk(\024)h Fp(0;)115 b Fo(i)27 b Fp(=)h(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(:)298 b Fp(\(5.11\))486 4188 y(T)-8 b(o)32 b(do)h(this)g(w)m(e)g(ma)m(y)h(replace)f FC(D)g Fp(b)m(y)g(the)g(mo)s (di\014ed)h(Heisen)m(b)s(erg)g(deriv)-5 b(ativ)m(e)859 4417 y FC(D)945 4432 y Fj(3)1012 4417 y Fp(=)1143 4349 y Fo(d)p 1126 4394 86 4 v 1126 4485 a(dt)1244 4417 y Fp(+)22 b Fo(i)1375 4336 y Fi(\002)1442 4391 y Fp(\026)1417 4417 y Fo(H)7 b(;)17 b Fk(\001)1577 4336 y Fi(\003)1618 4417 y Fp(;)1785 4391 y(\026)1759 4417 y Fo(H)35 b Fp(=)28 b Fo(L)2045 4432 y Fj(3)2085 4417 y Fo(H)8 b(L)2240 4432 y Fj(3)2279 4417 y Fo(;)114 b(L)2486 4432 y Fj(3)2554 4417 y Fp(=)27 b Fo(L)2723 4432 y Fj(3)2763 4417 y Fp(\()p Fo(t)p Fp(\))p Fo(;)386 4633 y Fp(cf.)44 b(\(5.4\))32 b(and)g(argumen)m(ts)i(b)s(elo)m(w)f(for)f(\(5.17\).)486 4749 y(With)38 b(this)h(mo)s(di\014cation)f(w)m(e)h(\014rst)g(lo)s(ok)f (at)g(the)g(most)h(in)m(teresting)g(b)s(ound)386 4865 y(\(5.11\))32 b(with)h Fo(i)28 b Fp(=)f(1.)44 b(W)-8 b(e)33 b(use)g(\(3.16\))f(to)g(write)513 5083 y FC(D)599 5098 y Fj(3)638 5083 y Fo(F)701 5098 y Fj(+)761 5083 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))27 b(=)h Fo(F)1235 5022 y Fn(0)1264 4995 y Fh(1)p 1264 5007 31 3 v 1264 5048 a(2)1221 5104 y Fj(+)1308 5083 y Fp(\()p Fo(B)5 b Fp(\()p Fo(t)p Fp(\)\))p Fo(D)s Fp(\()p Fo(t)p Fp(\))p Fo(F)1846 5022 y Fn(0)1875 4995 y Fh(1)p 1875 5007 V 1875 5048 a(2)1832 5104 y Fj(+)1920 5083 y Fp(\()o Fo(B)g Fp(\()q Fo(t)p Fp(\)\))22 b(+)g Fo(R)2380 5098 y Fj(1)2419 5083 y Fp(\()p Fo(t)p Fp(\))h(+)f Fo(R)2725 5098 y Fj(2)2764 5083 y Fp(\()p Fo(t)p Fp(\))h(+)f Fo(R)3070 5098 y Fj(3)3109 5083 y Fp(\()p Fo(t)p Fp(\);)513 5291 y Fo(D)s Fp(\()p Fo(t)p Fp(\))28 b(=)849 5223 y(2)22 b Fk(\000)h Fp(2)p Fo(\033)p 849 5268 279 4 v 971 5359 a(t)1137 5291 y(B)5 b Fp(\()p Fo(t)p Fp(\))23 b Fk(\000)f Fo(L)1515 5306 y Fj(3)1555 5210 y Fi(\010)1613 5291 y Fo(B)5 b Fp(\()p Fo(t)p Fp(\))17 b(Re)1952 5210 y Fi(\000)1999 5272 y Fp(~)1998 5291 y Fo(t)2033 5249 y Fn(\000)p Fj(1)2127 5210 y Fi(\001)2195 5291 y Fp(+)22 b Fo(h:c:)2445 5210 y Fi(\011)2503 5291 y Fo(L)2569 5306 y Fj(3)2609 5291 y Fo(:)489 b Fp(\(5.12\))386 5506 y(Notice)33 b(that)e(here)i Fo(R)1187 5521 y Fj(3)1227 5506 y Fp(\()p Fo(t)p Fp(\))f(is)g(giv)m(en) h(b)m(y)g(the)g(in)m(tegral)f(represen)m(tation)i(\(3.11\))d(of)386 5623 y(Lemma)36 b(3.5)f(in)g(terms)h(of)f(the)h(b)s(ounded)g(op)s (erator)e Fo(D)2449 5638 y Fm(r)2487 5623 y Fp(\()p Fo(t)p Fp(\))f(=)f FC(D)2825 5638 y Fj(3)2864 5623 y Fo(B)5 b Fp(\()p Fo(t)p Fp(\))24 b Fk(\000)h Fo(D)s Fp(\()p Fo(t)p Fp(\))p eop end %%Page: 26 26 TeXDict begin 26 25 bop 386 259 a Fl(26)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y Fp(whic)m(h)34 b(b)m(y)g(\(5.8\))e(is)h(of)f(the)h(form)487 711 y Fo(D)568 726 y Fm(r)606 711 y Fp(\()p Fo(t)p Fp(\))28 b(=)g Fo(\024)905 670 y Fn(\000)p Fj(2)999 711 y Fo(t)1034 670 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1234 644 y Fo(d)p 1217 688 86 4 v 1217 780 a(dt)1312 711 y(P)36 b Fp(+)1509 631 y Fi(\010)1567 711 y Fo(\024)1623 670 y Fn(\000)p Fj(2)1718 711 y Fo(t)1753 670 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1925 711 y Fo(L)1991 726 y Fj(3)2031 711 y Fo(H)8 b(i)p Fp([)p Fo(L)2246 726 y Fj(3)2286 711 y Fo(;)17 b(P)d Fp(])21 b(+)h Fo(h:c:)2705 631 y Fi(\011)509 932 y Fp(+)g Fo(\024)663 890 y Fn(\000)p Fj(2)758 932 y Fo(t)793 890 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)966 821 y Fi(n)1032 932 y Fp(Re)1164 851 y Fi(\000)1209 932 y Fo(GO)1364 851 y Fi(\000)1409 932 y Fo(t)1444 890 y Fn(\000)p Fj(2)1539 851 y Fi(\001)o(\001)1652 932 y Fp(+)g(Re)1882 851 y Fi(\000)1928 932 y Fo(G)2005 890 y Fn(\003)2044 932 y Fo(O)2122 851 y Fi(\000)2167 932 y Fo(t)2202 890 y Fn(\000)p Fj(2)2297 851 y Fi(\001)o(\001)2410 932 y Fp(+)g Fo(O)2586 821 y Fi(\020)2645 932 y Fo(t)2680 890 y Fj(2)p Fm(\027)2754 867 y Fc(0)2777 890 y Fn(\000)p Fj(3)2871 821 y Fi(\021o)2997 932 y Fo(:)3125 810 y Fp(\(5.13\))486 1157 y(First)32 b(w)m(e)i(examine)f(the)g(con)m(tribution)h(from)e(the) h(exp)s(ectation)g(of)f(the)h(term)1085 1358 y Fk(\001)17 b(\001)g(\001)e Fo(L)1284 1373 y Fj(2)1324 1358 y Fp(\()o Fo(s)p Fp(\))1445 1310 y Fj(2)1485 1358 y Fk(f)p Fo(R)1609 1373 y Fj(1)1648 1358 y Fp(\()p Fo(s)p Fp(\))22 b(+)g Fo(R)1964 1373 y Fj(2)2004 1358 y Fp(\()p Fo(s)p Fp(\))p Fk(g)p Fo(L)2242 1373 y Fj(1)2281 1358 y Fp(\()p Fo(s)p Fp(\))g(+)g Fo(h:c:)386 1557 y Fp(of)39 b(the)i(in)m(tegrand)f(of)g (\(5.11\))f(\(after)h(substituting)h(\(5.12\)\).)65 b(W)-8 b(e)40 b(ma)m(y)h(write,)386 1674 y(omitting)33 b(here)g(and)g (henceforth)g(the)g(argumen)m(t)g Fo(s)p Fp(,)965 1869 y Fo(i)p Fp([)p Fo(D)s(;)17 b(B)5 b Fp(])27 b(=)h Fk(\000)p Fo(i)1500 1788 y Fi(\002)1542 1869 y Fo(L)1608 1884 y Fj(3)1648 1788 y Fi(\010)1706 1869 y Fo(B)22 b Fp(Re)1933 1788 y Fi(\000)1980 1851 y Fp(~)1979 1869 y Fo(t)2014 1828 y Fn(\000)p Fj(1)2109 1788 y Fi(\001)2176 1869 y Fp(+)h Fo(h:c:)2427 1788 y Fi(\011)2485 1869 y Fo(L)2551 1884 y Fj(3)2591 1869 y Fo(;)17 b(B)2714 1788 y Fi(\003)992 2030 y Fp(=)28 b Fk(\000)1173 1949 y Fi(\000)1219 2030 y Fo(L)1285 2045 y Fj(3)1325 1949 y Fi(\010)1383 2030 y Fo(B)22 b Fp(Re)1610 1949 y Fi(\000)1657 2012 y Fp(~)1656 2030 y Fo(t)1691 1989 y Fn(\000)p Fj(1)1786 1949 y Fi(\001)1853 2030 y Fp(+)g Fo(h:c:)2103 1949 y Fi(\011)2162 2030 y Fo(i)p Fp([)p Fo(L)2288 2045 y Fj(3)2328 2030 y Fo(;)17 b(B)5 b Fp(])22 b(+)g Fo(h:c:)2750 1949 y Fi(\001)987 2191 y Fk(\000)g Fo(L)1152 2206 y Fj(3)1192 2110 y Fi(\010)1250 2191 y Fo(B)g Fp(Re)1478 2110 y Fi(\000)1523 2191 y Fo(i)1556 2110 y Fi(\002)1600 2173 y Fp(~)1598 2191 y Fo(t)1633 2150 y Fn(\000)p Fj(1)1728 2191 y Fo(;)17 b(B)1851 2110 y Fi(\003)o(\001)1960 2191 y Fp(+)22 b Fo(h:c:)2210 2110 y Fi(\011)2268 2191 y Fo(L)2334 2206 y Fj(3)2374 2191 y Fo(:)3125 2032 y Fp(\(5.14\))386 2396 y(Substituted)h(in)m(to)f(the)g (represen)m(tation)i(form)m(ulas)e(\(3.13\))f(and)h(\(3.14\))f(of)g (Lemma)386 2512 y(3.5)34 b(the)h(\014rst)g(term)f(to)g(the)h(righ)m(t)g (can)g(b)s(e)f(sho)m(wn)i(to)e(con)m(tribute)h(b)m(y)h(terms)f(of)386 2628 y(the)43 b(form)f Fo(\024)860 2592 y Fn(\000)p Fj(2)954 2628 y Fo(O)s Fp(\()o Fo(s)1115 2592 y Fn(\0001)1245 2628 y Fp(\))g(\(using)h(the)g(factors)f(of)g Fo(L)2320 2643 y Fj(1)2402 2628 y Fp(and)h Fo(L)2668 2643 y Fj(2)2750 2628 y Fp(and)f(comm)m(uta-)386 2749 y(tion\),)32 b(ho)m(w)m(ev)m(er)i (the)e(b)s(ound)f Fo(\024)1546 2713 y Fn(\000)p Fj(1)1641 2749 y Fo(O)1719 2668 y Fi(\000)1764 2749 y Fo(s)1810 2713 y Fm(\027)1849 2689 y Fc(0)1871 2713 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\033)2063 2668 y Fi(\001)2140 2749 y Fp(su\016ces.)46 b(Here)32 b(and)g(henceforth)386 2877 y Fo(O)464 2796 y Fi(\000)509 2877 y Fo(s)555 2841 y Fn(\000)q Fj(~)-36 b Fm(\017)642 2796 y Fi(\001)718 2877 y Fp(refers)31 b(to)e(a)h(term)g(b)s(ounded)h(b)m(y)g Fo(C)7 b(s)2056 2841 y Fn(\000)q Fj(~)-36 b Fm(\017)2173 2877 y Fp(uniformly)31 b(in)f Fo(t)g Fp(\(recall)h(that)f Fo(B)386 2999 y Fp(con)m(tains)38 b(a)g(factor)f Fo(\024)1200 2963 y Fn(\000)p Fj(2)1330 2999 y Fp(=)f Fo(t)1477 2963 y Fn(\000)p Fj(2)p Fm(\017)1600 2999 y Fp(\).)58 b(T)-8 b(o)38 b(demonstrate)g(this)h(w)m(eak)m(er)g(b)s(ound)f(w)m(e)386 3115 y(compute)683 3314 y Fo(i)p Fp([)p Fo(L)809 3329 y Fj(3)849 3314 y Fo(;)17 b(B)5 b Fp(])28 b(=)f Fo(\024)1186 3273 y Fn(\000)p Fj(1)1281 3314 y Fo(s)1327 3273 y Fj(1)p Fn(\000)p Fm(\033)1464 3314 y Fo(i)p Fp([)p Fo(L)1590 3329 y Fj(3)1630 3314 y Fo(;)17 b(G)p Fp(])1800 3289 y(\026)1778 3314 y Fo(G)1855 3273 y Fn(\003)1916 3314 y Fp(+)22 b Fo(\024)2070 3273 y Fn(\000)p Fj(1)2165 3314 y Fo(s)2211 3273 y Fj(1)p Fn(\000)p Fm(\033)2370 3289 y Fp(\026)2348 3314 y Fo(G)2425 3273 y Fn(\003)2464 3314 y Fo(i)p Fp([)p Fo(L)2590 3329 y Fj(3)2630 3314 y Fo(;)17 b(G)p Fp(])22 b(+)g Fo(h:c:;)683 3505 y(i)p Fp([)p Fo(L)809 3520 y Fj(3)849 3505 y Fo(;)17 b(G)p Fp(])28 b(=)f Fo(O)1206 3394 y Fi(\020)1265 3505 y Fo(s)1311 3464 y Fm(\027)1350 3441 y Fc(0)1372 3464 y Fn(\000)p Fj(1)1467 3394 y Fi(\021)1526 3505 y Fo(:)386 3746 y Fp(Since)34 b(the)f(middle)g(factor)f(Re)1539 3665 y Fi(\000)1586 3727 y Fp(~)1585 3746 y Fo(t)1620 3709 y Fn(\000)p Fj(1)1714 3665 y Fi(\001)1788 3746 y Fp(=)27 b Fo(O)s Fp(\()p Fo(s)2053 3709 y Fn(\000)p Fj(1)2147 3746 y Fp(\))32 b(w)m(e)i(get)e(the)h(b)s(ound)1056 3964 y Fo(\024)1112 3923 y Fn(\000)p Fj(1)1206 3964 y Fo(O)1284 3883 y Fi(\000)1329 3964 y Fo(s)1375 3923 y Fj(1)p Fn(\000)p Fm(\033)1512 3883 y Fi(\001)1558 3964 y Fo(O)1636 3883 y Fi(\000)1681 3964 y Fo(s)1727 3923 y Fm(\027)1766 3899 y Fc(0)1788 3923 y Fn(\000)p Fj(2)1882 3883 y Fi(\001)1956 3964 y Fp(=)27 b Fo(\024)2115 3923 y Fn(\000)p Fj(1)2210 3964 y Fo(O)2288 3883 y Fi(\000)2333 3964 y Fo(s)2379 3923 y Fm(\027)2418 3899 y Fc(0)2440 3923 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\033)2632 3883 y Fi(\001)2678 3964 y Fo(:)386 4171 y Fp(W)-8 b(e)38 b(used)g(that)1025 4146 y(\026)1003 4171 y Fo(G;)1243 4146 y Fp(\026)1221 4171 y Fo(G)1298 4135 y Fn(\003)1375 4171 y Fp(and)f Fo(B)43 b Fp(ma)m(y)38 b(b)s(e)g(considered)h(as)f(b)s(ounded)g(in)g(com-)386 4288 y(bination)d(with)h(the)g(resolv)m(en)m(ts)i(of)d Fo(B)5 b Fp(;)36 b(explicitly)i(w)m(e)e(exploited)h(the)e(uniform)386 4404 y(b)s(ounds)e(\(after)f(comm)m(utation\))719 4686 y Fk(jj)796 4660 y Fp(\026)775 4686 y Fo(G)o Fp(\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))1178 4637 y Fn(\000)p Fj(1)1272 4686 y Fk(jj)p Fo(;)113 b Fk(jj)1546 4660 y Fp(\026)1524 4686 y Fo(G)1601 4644 y Fn(\003)1640 4686 y Fp(\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))1967 4637 y Fn(\000)p Fj(1)2061 4686 y Fk(jj)k(\024)h Fo(C)2345 4618 y Fk(h)p Fo(z)t Fk(i)2472 4570 y Fj(1)p Fm(=)p Fj(2)p 2336 4663 255 4 v 2336 4754 a Fk(j)17 b Fp(Im)g Fo(z)t Fk(j)2601 4686 y Fo(;)719 4907 y Fk(jj)p Fp(\()o Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))1101 4859 y Fn(\000)p Fj(1)1195 4907 y Fk(jj)k(\024)h Fo(C)7 b Fk(j)17 b Fp(Im)f Fo(z)t Fk(j)1714 4866 y Fn(\000)p Fj(1)1809 4907 y Fo(;)114 b Fk(jj)p Fo(B)5 b Fp(\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))2411 4859 y Fn(\000)p Fj(1)2506 4907 y Fk(jj)k(\024)h Fo(C)r(:)3125 4758 y Fp(\(5.15\))486 5107 y(Similarly)-8 b(,)33 b(since)544 5306 y(Re)676 5225 y Fi(\000)722 5306 y Fo(i)755 5225 y Fi(\002)798 5287 y Fp(~)796 5306 y Fo(t)831 5265 y Fn(\000)p Fj(1)926 5306 y Fo(;)17 b(B)1049 5225 y Fi(\003)o(\001)1164 5306 y Fp(=)27 b Fo(\024)1323 5265 y Fn(\000)p Fj(1)1418 5306 y Fo(O)1496 5225 y Fi(\000)1541 5306 y Fo(s)1587 5265 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\033)1779 5225 y Fi(\001)1846 5281 y Fp(\026)1824 5306 y Fo(G)1901 5265 y Fn(\003)1963 5306 y Fp(+)22 b Fo(\024)2117 5265 y Fn(\000)p Fj(1)2211 5306 y Fo(O)2289 5225 y Fi(\000)2334 5306 y Fo(s)2380 5265 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\033)2572 5225 y Fi(\001)2640 5281 y Fp(\026)2618 5306 y Fo(G)g Fp(+)g Fo(h:c:)158 b Fp(\(5.16\))386 5506 y(the)27 b(second)h(term)g (to)e(the)i(righ)m(t)f(in)g(\(5.14\))f(con)m(tributes)i(b)m(y)g(a)f (term)g(of)g(the)g(form)386 5623 y Fo(\024)442 5587 y Fn(\000)p Fj(1)536 5623 y Fo(O)s Fp(\()p Fo(s)698 5587 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\033)889 5623 y Fp(\).)p eop end %%Page: 27 27 TeXDict begin 27 26 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(27)486 459 y Fp(Using)32 b(the)g(represen)m(tation)i (for)d Fo(R)1785 474 y Fj(3)1852 459 y Fp(=)d Fo(R)2030 474 y Fj(3)2069 459 y Fp(\()p Fo(s)p Fp(\))k(and)g(comm)m(utation)g(w)m (e)h(claim)386 575 y(the)g(b)s(ound)486 762 y Fk(\001)17 b(\001)g(\001)d Fo(L)684 721 y Fj(2)684 787 y(2)724 762 y Fo(R)798 777 y Fj(3)838 762 y Fo(L)904 777 y Fj(1)966 762 y Fp(+)22 b Fo(h:c:)939 953 y Fp(=)27 b Fo(\024)1098 912 y Fn(\000)p Fj(1)1193 953 y Fo(O)1271 873 y Fi(\000)1316 953 y Fo(s)1362 912 y Fn(\000)p Fj(1)1456 873 y Fi(\001)1524 953 y Fp(+)22 b Fo(\024)1678 912 y Fn(\000)p Fj(1)1772 953 y Fo(O)1850 873 y Fi(\000)1895 953 y Fo(s)1941 912 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\033)2133 873 y Fi(\001)2201 953 y Fp(+)g Fo(\024)2355 912 y Fn(\000)p Fj(2)2449 953 y Fo(O)2527 843 y Fi(\020)2586 953 y Fo(s)2632 912 y Fj(2)p Fm(\027)2706 889 y Fc(0)2729 912 y Fn(\000)p Fj(1)p Fn(\000)p Fj(2)p Fm(\033)2956 843 y Fi(\021)3015 953 y Fo(:)83 b Fp(\(5.17\))386 1148 y(The)44 b(con)m(tributions)g(from)f (the)h(\014rst)f(t)m(w)m(o)h(terms)g(of)e(\(5.13\))h(are)g Fo(\024)2952 1111 y Fn(\000)p Fj(2)3046 1148 y Fo(O)s Fp(\()o Fo(s)3207 1111 y Fn(\0001)3337 1148 y Fp(\))386 1264 y(and)29 b(therefore)i(in)e(particular)h Fo(\024)1592 1228 y Fn(\000)p Fj(1)1686 1264 y Fo(O)s Fp(\()p Fo(s)1848 1228 y Fn(\000)p Fj(1)1942 1264 y Fp(\).)42 b(Let)30 b(us)g(elab)s(orate)f(on)h(this)g(w)m(eak)m(er)386 1380 y(b)s(ound)j(for)f(the)h(\014rst)g(term:)44 b(W)-8 b(rite)773 1575 y Fo(\024)829 1534 y Fn(\000)p Fj(2)923 1575 y Fo(s)969 1534 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1174 1508 y Fo(d)p 1151 1552 97 4 v 1151 1643 a(ds)1258 1575 y(P)41 b Fp(=)28 b Fo(\024)1522 1534 y Fn(\000)p Fj(1)1616 1575 y Fo(s)1662 1534 y Fj(1)p Fn(\000)p Fm(\033)1799 1435 y Fi(\032)1896 1550 y Fp(\026)1874 1575 y Fo(G)1984 1508 y(d)p 1961 1552 V 1961 1643 a(ds)2067 1575 y(G)2144 1534 y Fn(\003)2206 1575 y Fp(+)2326 1550 y(\026)2304 1575 y Fo(G)2381 1534 y Fn(\003)2453 1508 y Fo(d)p 2430 1552 V 2430 1643 a(ds)2537 1575 y(G)22 b Fp(+)g Fo(h:c:)2886 1435 y Fi(\033)2961 1575 y Fo(;)386 1810 y Fp(and)40 b(compute)g(the)h(time-deriv)-5 b(ativ)m(e)41 b(of)e(the)h(sym)m(b)s(ol)2475 1786 y(~)2475 1810 y(~)-53 b Fo(g)2518 1825 y Fj(1)2557 1810 y Fp(\()p Fo(s)2641 1773 y Fn(\000)p Fj(1)2735 1810 y Fo(x)p Fp(\))40 b(that)g(de\014nes)386 1926 y(the)33 b(time-dep)s(endence)i(of)d(the)h (sym)m(b)s(ol)h(of)e Fo(G)1143 2065 y(d)p 1120 2109 V 1120 2201 a(ds)1230 2109 y Fp(~)1230 2132 y(~)-52 b Fo(g)1274 2147 y Fj(1)1313 2051 y Fi(\000)1358 2132 y Fo(s)1404 2091 y Fn(\000)p Fj(1)1499 2132 y Fo(x)1554 2051 y Fi(\001)1627 2132 y Fp(=)28 b Fk(\000)p Fo(s)1854 2091 y Fn(\000)p Fj(2)1949 2132 y Fo(x)22 b Fk(\001)2076 2051 y Fi(\000)2122 2132 y Fk(r)2208 2109 y Fp(~)2208 2132 y(~)-52 b Fo(g)2252 2147 y Fj(1)2291 2051 y Fi(\001\000)2382 2132 y Fo(s)2428 2091 y Fn(\000)p Fj(1)2522 2132 y Fo(x)2577 2051 y Fi(\001)2624 2132 y Fo(:)386 2320 y Fp(The)44 b(con)m(tribution)g(from)e(this)i (expression)h(is)e(treated)h(b)m(y)f(using)h(the)f(factor)386 2436 y Fo(g)433 2451 y Fj(1)472 2436 y Fp(\()p Fo(s)556 2400 y Fn(\000)p Fj(1)650 2436 y Fo(x)p Fp(\))24 b(of)g Fo(L)936 2451 y Fj(1)976 2436 y Fp(.)40 b(First)24 b(w)m(e)h(ma)m(y)f (insert)h(the)f Fo(j)6 b Fp('th)24 b(p)s(o)m(w)m(er)h(of)e Fo(F)42 b Fp(=)31 b(~)-53 b Fo(g)2853 2451 y Fj(1)2892 2436 y Fp(\()p Fo(s)2976 2400 y Fn(\000)p Fj(1)3071 2436 y Fo(x)p Fp(\))24 b(next)386 2553 y(to)j(a)g(factor)g Fo(L)916 2568 y Fj(1)956 2553 y Fp(.)41 b(Then)29 b(w)m(e)f(place)g (one)g(factor)f(of)g Fo(F)41 b Fp(next)28 b(to)f(an)m(y)h(of)f(the)h (factors)386 2669 y(of)33 b(the)i(time-deriv)-5 b(ativ)m(e)35 b(of)f Fo(G)f Fp(b)m(y)i(comm)m(uting)g(through)f(the)g(resolv)m(en)m (t)i(of)d Fo(B)5 b Fp(,)386 2785 y(and)35 b(rep)s(eat)h(successiv)m (ely)j(this)d(pro)s(cedure)g(for)f(the)h(\\errors")f(giv)m(en)h(in)g (terms)386 2901 y(of)46 b(in)m(termediary)i(comm)m(utators.)86 b(A)m(t)47 b(eac)m(h)g(step)g(a)f(factor)g(of)g Fo(\024)2944 2865 y Fn(\000)p Fj(1)3039 2901 y Fo(s)3085 2865 y Fm(\027)3124 2842 y Fc(0)3146 2865 y Fn(\000)p Fm(\033)3299 2901 y Fp(=)386 3018 y Fo(O)464 2937 y Fi(\000)509 3018 y Fo(s)555 2981 y Fm(\027)594 2958 y Fc(0)616 2981 y Fn(\000)p Fm(\033)718 2937 y Fi(\001)804 3018 y Fp(will)c(b)s(e)f(gained.)68 b(\(In)41 b(fact)g(for)f(the)h(\014rst)h(term)f(of)f(\(5.13\))g (treated)386 3145 y(here)i(w)m(e)g(ha)m(v)m(e)h(the)e(stronger)h (estimate)g Fo(O)2034 3065 y Fi(\000)2079 3145 y Fo(s)2125 3109 y Fn(\000)p Fm(\033)2227 3065 y Fi(\001)2273 3145 y Fp(.\))69 b(This)42 b(means)h(that)e(if)g(w)m(e)386 3276 y(put)36 b Fo(\033)627 3240 y Fn(0)684 3276 y Fp(=)d Fo(\033)28 b Fk(\000)d Fo(\027)1032 3240 y Fn(0)1092 3276 y Fp(then)37 b Fo(h)c Fp(=)g Fo(s)1562 3240 y Fn(\000)p Fm(\033)1659 3216 y Fc(0)1722 3276 y Fp(will)k(b)s(e)f(an)g (\\e\013ectiv)m(e)h(Planc)m(k)h(constan)m(t".)386 3392 y(Notice)33 b(that)456 3551 y Fo(i)506 3470 y Fi(\002)548 3551 y Fp(\()p Fo(B)27 b Fk(\000)22 b Fo(z)t Fp(\))874 3502 y Fn(\000)p Fj(1)968 3551 y Fo(;)17 b(F)1089 3470 y Fi(\003)484 3741 y Fp(=)27 b Fo(\024)643 3700 y Fn(\000)p Fj(1)738 3741 y Fo(s)784 3700 y Fj(1)p Fn(\000)p Fm(\033)921 3741 y Fp(\()p Fo(B)g Fk(\000)c Fo(z)t Fp(\))1247 3693 y Fn(\000)p Fj(1)1342 3631 y Fi(n)1430 3716 y Fp(\026)1408 3741 y Fo(GO)1563 3631 y Fi(\020)1622 3741 y Fo(s)1668 3700 y Fm(\027)1707 3677 y Fc(0)1729 3700 y Fn(\000)p Fj(1)1824 3631 y Fi(\021)1905 3741 y Fp(+)2025 3716 y(\026)2003 3741 y Fo(G)2080 3700 y Fn(\003)2120 3741 y Fo(O)2198 3631 y Fi(\020)2256 3741 y Fo(s)2302 3700 y Fm(\027)2341 3677 y Fc(0)2364 3700 y Fn(\000)p Fj(1)2458 3631 y Fi(\021)2540 3741 y Fp(+)f Fo(h:c:)2790 3631 y Fi(o)2856 3741 y Fp(\()p Fo(B)28 b Fk(\000)22 b Fo(z)t Fp(\))3183 3693 y Fn(\000)p Fj(1)3277 3741 y Fo(:)386 3926 y Fp(Rep)s(eated)47 b(comm)m(utation)h (through)f(suc)m(h)h(an)f(expression)i(b)m(y)f(factors)f(of)f Fo(F)386 4042 y Fp(pro)m(vides)35 b(ev)m(en)m(tually)h(the)e(p)s(o)m(w) m(er)h Fo(h)1750 4006 y Fm(j)1816 4042 y Fp(=)29 b Fo(s)1967 4006 y Fn(\000)p Fm(\033)2064 3983 y Fc(0)2087 4006 y Fm(j)2124 4042 y Fp(.)46 b(Again)33 b(the)h(\014nite)h(n)m(um)m(b)s (ers)g(of)386 4161 y(factors)h(lik)m(e)911 4136 y(\026)889 4161 y Fo(G)p Fp(\()p Fo(B)27 b Fk(\000)c Fo(z)t Fp(\))1292 4113 y Fn(\000)p Fj(1)1422 4161 y Fp(and)1637 4136 y(\026)1615 4161 y Fo(G)1692 4125 y Fn(\003)1732 4161 y Fp(\()o Fo(B)28 b Fk(\000)22 b Fo(z)t Fp(\))2058 4113 y Fn(\000)p Fj(1)2188 4161 y Fp(ma)m(y)37 b(b)s(e)f(estimated)h(b)m(y)f(\(5.15\))386 4277 y(b)s(efore)30 b(in)m(tegrating)g(with)h(resp)s(ect)g(to)f(the)g Fo(z)t Fp({v)-5 b(ariable.)44 b(W)-8 b(e)30 b(c)m(ho)s(ose)h Fo(j)36 b Fp(so)30 b(large)386 4394 y(that)i Fo(\033)656 4357 y Fn(0)680 4394 y Fp(\()p Fo(j)c Fp(+)22 b(1\))27 b Fk(\025)h Fp(1.)486 4510 y(The)40 b(con)m(tribution)h(to)f(\(5.17\))f (from)h(the)g(second)i(term)e(of)f(\(5.13\))h(ma)m(y)g(b)s(e)386 4626 y(treated)33 b(v)m(ery)h(similarly)-8 b(.)486 4742 y(Clearly)39 b(the)g(last)f(term)h(of)f(\(5.13\))g(con)m(tributes)i(b)m (y)f(terms)g(of)f(the)h(form)f(of)386 4858 y(the)33 b(last)g(t)m(w)m(o) g(terms)g(to)g(the)g(righ)m(t)f(in)h(\(5.17\).)486 4975 y(Next)f(w)m(e)h(mo)m(v)m(e)g(the)f(factors)g(of)f Fo(L)1777 4990 y Fj(2)1849 4975 y Fp(next)h(to)g(those)g(of)g Fo(L)2617 4990 y Fj(1)2688 4975 y Fp(\(and)g(other)g(com-)386 5091 y(m)m(utation\))27 b(for)g(the)g(con)m(tribution)i(to)d(\(5.11\))h (from)f(the)i(\014rst)g(term)f(to)g(the)g(righ)m(t)386 5207 y(in)33 b(\(5.12\))f(yielding,)h(as)g(a)g(conclusion,)h(that)658 5397 y Fk(h)p Fo(T)754 5412 y Fj(1)810 5397 y Fp(\()p Fo(s;)17 b(\024)p Fp(\))p Fk(i)1071 5426 y Fm(s)1135 5397 y Fk(\024)1240 5287 y Fi(D)1321 5371 y Fp(\025)1301 5397 y Fo( )t(;)g(D)s Fp(\()o Fo(s)p Fp(\))1637 5371 y(\025)1617 5397 y Fo( )1684 5287 y Fi(E)1767 5397 y Fp(+)22 b Fo(\024)1921 5356 y Fn(\000)p Fj(1)2016 5397 y Fo(O)2094 5316 y Fi(\000)2139 5397 y Fo(s)2185 5356 y Fn(\000)p Fj(1)2279 5316 y Fi(\001)2347 5397 y Fp(+)g Fo(O)2523 5287 y Fi(\020)2582 5397 y Fo(s)2628 5356 y Fm(\027)2667 5333 y Fc(0)2689 5356 y Fn(\000)p Fj(2)2783 5287 y Fi(\021)2843 5397 y Fp(;)661 5591 y(\025)642 5617 y Fo( )31 b Fp(=)840 5536 y Fi(\000)885 5617 y Fo(F)962 5576 y Fj(2)p Fn(0)948 5642 y Fj(+)1021 5536 y Fi(\001)1076 5531 y Fh(1)p 1076 5543 31 3 v 1076 5585 a(2)1121 5617 y Fp(\()p Fo(B)5 b Fp(\()p Fo(s)p Fp(\)\))p Fo(L)1464 5632 y Fj(2)1504 5617 y Fp(\()o Fo(s)p Fp(\))p Fo(L)1691 5632 y Fj(1)1731 5617 y Fp(\()p Fo(s)p Fp(\))p Fo( )t Fp(\()p Fo(s)p Fp(\))p Fo(:)3125 5494 y Fp(\(5.18\))p eop end %%Page: 28 28 TeXDict begin 28 27 bop 386 259 a Fl(28)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 495 y Fp(Notice)33 b(that)f(comm)m(utation)g(of)g Fo(D)s Fp(\()p Fo(s)p Fp(\))g(with)g(the)h(factors)f(of)g Fo(L)2727 510 y Fj(2)2766 495 y Fp(\()p Fo(s)p Fp(\),)h Fo(F)3025 435 y Fn(0)3054 408 y Fh(1)p 3053 420 31 3 v 3053 461 a(2)3011 517 y Fj(+)3098 495 y Fp(\()p Fo(B)5 b Fp(\()p Fo(s)p Fp(\)\))386 650 y(and)568 569 y Fi(\000)614 650 y Fo(F)691 614 y Fj(2)p Fn(0)677 675 y Fj(+)749 569 y Fi(\001)805 564 y Fh(1)p 805 576 V 805 618 a(2)850 650 y Fp(\()p Fo(B)g Fp(\()p Fo(s)p Fp(\))o(\))26 b(\(when)g(symmetrizing\))i(in)m(v)m(olv)m (es)g(the)e(calculus)h(of)e(Lemma)386 780 y(3.5)36 b(and)h(the)f (e\013ectiv)m(e)j(Planc)m(k)f(constan)m(t)f Fo(h)e Fp(=)f Fo(s)2262 744 y Fn(\000)p Fm(\033)2359 721 y Fc(0)2423 780 y Fp(in)i(a)h(similar)g(fashion)f(as)386 897 y(ab)s(o)m(v)m(e.)486 1013 y(F)-8 b(or)27 b(the)i(\014rst)g(term)g(on)f(the)h(righ)m(t)f (hand)h(side)g(of)f(\(5.18\))g(w)m(e)h(infer)g(from)f(\(5.6\))386 1129 y(and)33 b(\(5.9\))f(that)1097 1216 y Fi(D)1177 1300 y Fp(\025)1157 1326 y Fo( )t(;)17 b(D)s Fp(\()p Fo(s)p Fp(\))1494 1300 y(\025)1474 1326 y Fo( )1541 1216 y Fi(E)1629 1326 y Fk(\024)28 b Fo(C)1804 1341 y Fj(1)1844 1326 y Fo(\024)1900 1285 y Fn(\000)p Fj(2)1994 1326 y Fo(s)2040 1285 y Fn(\000)p Fj(1)p Fn(\000)p Fj(2)p Fm(\033)2289 1326 y Fp(+)22 b Fo(C)2457 1341 y Fj(2)2497 1326 y Fo(s)2543 1285 y Fn(\000)p Fj(2)2637 1326 y Fo(:)461 b Fp(\(5.19\))386 1523 y(By)33 b(com)m(bining)h(\(5.18\))e(and)g(\(5.19\))g(w)m(e)i (\014nally)f(conclude)h(\(5.11\))e(for)g Fo(i)c Fp(=)f(1.)486 1639 y(As)45 b(for)f(\(5.11\))f(for)h Fo(i)k Fp(=)g(2)c(w)m(e)i(use)f (Remark)h(4.3,)h(the)e(in)m(tegral)f(estimate)386 1756 y(of)f(Lemma)i(4.5)f(and)g(the)g(factors)g(of)g Fo(L)1935 1771 y Fj(1)1975 1756 y Fp(.)77 b(Notice)45 b(that)f(the)g(leading)h (\(clas-)386 1872 y(sical\))50 b(term)f(from)g(di\013eren)m(tiating)h (the)g(sym)m(b)s(ol)g Fo(b)2375 1887 y Fm(t)2454 1872 y Fp(ma)m(y)g(b)s(e)g(written)g(as)f(a)386 1988 y(sum)41 b(of)f(three)h(terms:)60 b(The)41 b(con)m(tribution)g(from)g (\\di\013eren)m(tiating")g(the)f(fac-)386 2104 y(tor)f Fo(F)613 2119 y Fn(\000)673 2104 y Fp(\()o Fo(t)745 2068 y Fm(\027)789 2104 y Fo(q)836 2068 y Fn(\000)895 2104 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o(\))40 b(is)g(non-p)s(ositiv)m(e,) j(cf.)66 b(Remark)40 b(4.3.)65 b(The)41 b(con)m(tribution)386 2222 y(from)32 b(\\di\013eren)m(tiating")h(the)f(\014rst)h(factor)f Fo(F)2052 2237 y Fn(\000)2111 2142 y Fi(\000)2157 2222 y Fo(t)2192 2186 y Fj(2)p Fm(\016)2265 2222 y Fo(q)2312 2186 y Fm(s)2349 2222 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2571 2142 y Fi(\001)2649 2222 y Fp(ma)m(y)33 b(after)f(a)g(sym-)386 2338 y(metrization)52 b(b)s(e)g(treated)g(b)m(y)h(Lemma)f(4.5.)101 b(The)52 b(comm)m(utation)h(through)386 2455 y(the)38 b(factors)f(of)g Fo(F)1060 2470 y Fj(+)1119 2455 y Fp(\()p Fo(B)5 b Fp(\()p Fo(s)p Fp(\)\))37 b(\(when)i(symmetrizing\))g(in)m(v)m (olv)m(es)h(the)e(calculus)h(of)386 2571 y(Lemma)28 b(3.5)f(in)h(a)f (similar)h(fashion)g(as)f(ab)s(o)m(v)m(e.)43 b(Finally)28 b(the)g(con)m(tribution)g(from)386 2687 y(\\di\013eren)m(tiating")37 b(the)f(last)h(t)m(w)m(o)g(factors)f(are)g(in)m(tegrable)h(due)g(to)f (the)h(factors)386 2803 y(of)32 b Fo(L)563 2818 y Fj(1)603 2803 y Fp(.)43 b(W)-8 b(e)33 b(omit)g(further)g(details.)486 2920 y(As)k(for)f(\(5.11\))g(for)g Fo(i)g Fp(=)e(3)j(w)m(e)h(use)f(the) h(in)m(tegral)f(estimate)h(\(1.9\))e(and)h(com-)386 3036 y(m)m(utation.)44 b(W)-8 b(e)33 b(omit)f(the)h(details.)486 3152 y(W)-8 b(e)25 b(conclude)h(\(5.11\),)g(and)f(therefore)h(b)m(y)g (Prop)s(osition)f(4.6)g(the)g(b)s(ound)g(\(5.7\))386 3268 y(\014rst)34 b(with)g Fo(\033)j Fp(replaced)e(b)m(y)f Fo(\033)27 b Fp(+)22 b Fo(\017)34 b Fp(and)g(then)g(\(since)g Fo(\017)g Fp(is)g(arbitrary\))f(b)m(y)i(an)m(y)f Fo(\033)386 3385 y Fp(as)f(sp)s(eci\014ed)h(in)f(the)g(prop)s(osition.)1609 b Fe(\003)386 3564 y FC(Corollary)38 b(5.2.)i Fg(Under)34 b(the)f(c)-5 b(onditions)32 b(of)h(Pr)-5 b(op)g(osition)33 b(5.1)g(and)g(with)g Fp(\000)28 b(=)386 3680 y(\000)447 3695 y Fm(t)504 3680 y Fp(=)g(Re)16 b(\()p Fo(G)p Fp(\))1129 3722 y Fi(\015)1129 3782 y(\015)1185 3807 y Fo(F)1248 3822 y Fj(+)1307 3726 y Fi(\000)1352 3807 y Fo(t)1387 3765 y Fj(1)p Fn(\000)p Fm(\033)1525 3807 y Fk(j)p Fp(\000)p Fk(j)1642 3726 y Fi(\001)1687 3807 y Fo( )t Fp(\()p Fo(t)p Fp(\))1865 3722 y Fi(\015)1865 3782 y(\015)1948 3807 y Fk(!)27 b Fp(0)35 b Fg(for)f Fo(t)28 b Fk(!)g(1)p Fo(:)493 b Fp(\(5.20\))386 3987 y Fg(Pr)-5 b(o)g(of.)41 b Fp(Let)33 b Fo(\033)g Fk(2)d Fp(\(2)p Fo(\027)1184 3951 y Fn(0)1207 3987 y Fo(;)17 b Fp(1\))33 b(b)s(e)g(giv)m(en.)47 b(Fix)33 b Fo(\033)2029 4002 y Fj(1)2098 3987 y Fk(2)c Fp(\(2)p Fo(\027)2334 3951 y Fn(0)2358 3987 y Fo(;)17 b(\033)t Fp(\))o(.)46 b(By)34 b(Prop)s(osition)f(5.1)386 4104 y(it)f(su\016ces)j(to)d(sho)m(w)i(that)1040 4185 y Fi(\015)1040 4244 y(\015)1095 4269 y Fo(F)1158 4284 y Fj(+)1217 4189 y Fi(\000)1263 4269 y Fo(t)1298 4228 y Fj(1)p Fn(\000)p Fm(\033)1435 4269 y Fk(j)p Fp(\000)p Fk(j)1552 4189 y Fi(\001)1597 4269 y Fo(F)1660 4284 y Fn(\000)1719 4189 y Fi(\000)1765 4269 y Fo(t)1800 4228 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1965 4237 y Fh(1)2005 4269 y Fo(P)2082 4189 y Fi(\001)2127 4185 y(\015)2127 4244 y(\015)2210 4269 y Fp(=)27 b Fo(O)2391 4189 y Fi(\000)2436 4269 y Fo(t)2471 4228 y Fm(\033)2511 4237 y Fh(1)2546 4228 y Fn(\000)p Fm(\033)2648 4189 y Fi(\001)2694 4269 y Fo(:)486 4435 y Fp(Clearly)33 b(b)m(y)h(the)f(sp)s(ectral)g(theorem)g(this)h (estimate)f(follo)m(ws)h(from)1323 4516 y Fi(\015)1323 4575 y(\015)1378 4600 y Fo(t)1413 4559 y Fj(1)p Fn(\000)p Fm(\033)1543 4568 y Fh(1)1583 4600 y Fp(\000)p Fo(F)1707 4615 y Fn(\000)1766 4520 y Fi(\000)1812 4600 y Fo(t)1847 4559 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)2012 4568 y Fh(1)2051 4600 y Fo(P)2128 4520 y Fi(\001)2174 4516 y(\015)2174 4575 y(\015)2257 4600 y Fk(\024)28 b Fp(1)p Fo(;)386 4772 y Fp(whic)m(h)47 b(in)f(turn)g(follo)m(ws)g(from)g(substituting)h (\000)i(=)h(2)2453 4736 y Fn(\000)p Fj(1)2547 4772 y Fp(\()p Fo(G)22 b Fp(+)g Fo(G)2859 4736 y Fn(\003)2899 4772 y Fp(\))45 b(and)h(then)386 4888 y(estimating)505 4969 y Fi(\015)505 5029 y(\015)561 5053 y Fo(t)596 5012 y Fj(1)p Fn(\000)p Fm(\033)726 5021 y Fh(1)765 5053 y Fp(\000)p Fo(F)889 5068 y Fn(\000)948 4973 y Fi(\000)994 5053 y Fo(t)1029 5012 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1194 5021 y Fh(1)1234 5053 y Fo(P)1311 4973 y Fi(\001)1356 4969 y(\015)1356 5029 y(\015)533 5215 y Fk(\024)28 b Fp(2)687 5173 y Fn(\000)p Fj(1)781 5130 y Fi(\015)781 5190 y(\015)837 5215 y Fo(t)872 5173 y Fj(1)p Fn(\000)p Fm(\033)1002 5182 y Fh(1)1041 5215 y Fo(GF)1181 5230 y Fn(\000)1240 5215 y Fp(\()p Fk(\001)p Fp(\))1344 5130 y Fi(\015)1344 5190 y(\015)1421 5215 y Fp(+)22 b(2)1568 5173 y Fn(\000)p Fj(1)1662 5130 y Fi(\015)1662 5190 y(\015)1718 5215 y Fo(t)1753 5173 y Fj(1)p Fn(\000)p Fm(\033)1883 5182 y Fh(1)1922 5215 y Fo(G)1999 5173 y Fn(\003)2039 5215 y Fo(F)2102 5230 y Fn(\000)2161 5215 y Fp(\()p Fk(\001)p Fp(\))2264 5130 y Fi(\015)2264 5190 y(\015)533 5399 y Fk(\024)28 b Fp(2)687 5358 y Fn(\000)p Fj(1)781 5314 y Fi(\015)781 5374 y(\015)837 5399 y Fo(t)872 5358 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1037 5367 y Fh(1)1077 5399 y Fo(F)1140 5414 y Fn(\000)1199 5399 y Fp(\()p Fk(\001)p Fp(\))o Fo(G)1379 5358 y Fn(\003)1419 5399 y Fo(GF)1559 5414 y Fn(\000)1618 5399 y Fp(\()p Fk(\001)p Fp(\))1721 5314 y Fi(\015)1721 5374 y(\015)1777 5341 y Fj(1)p Fm(=)p Fj(2)1909 5399 y Fp(+)22 b(2)2056 5358 y Fn(\000)p Fj(1)2150 5314 y Fi(\015)2150 5374 y(\015)2205 5399 y Fo(t)2240 5358 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)2405 5367 y Fh(1)2445 5399 y Fo(F)2508 5414 y Fn(\000)2567 5399 y Fp(\()p Fk(\001)p Fp(\))p Fo(GG)2825 5358 y Fn(\003)2864 5399 y Fo(F)2927 5414 y Fn(\000)2986 5399 y Fp(\()p Fk(\001)p Fp(\))3090 5314 y Fi(\015)3090 5374 y(\015)3145 5341 y Fj(1)p Fm(=)p Fj(2)533 5584 y Fk(\024)638 5499 y Fi(\015)638 5559 y(\015)694 5584 y Fo(F)757 5599 y Fn(\000)816 5584 y Fp(\()p Fk(\001)p Fp(\))o Fo(t)954 5543 y Fj(2)p Fn(\000)p Fj(2)p Fm(\033)1119 5552 y Fh(1)1159 5584 y Fo(P)14 b(F)1299 5599 y Fn(\000)1358 5584 y Fp(\()p Fk(\001)p Fp(\))1461 5499 y Fi(\015)1461 5559 y(\015)1517 5525 y Fj(1)p Fm(=)p Fj(2)1654 5584 y Fk(\024)28 b Fp(1)p Fo(:)p eop end %%Page: 29 29 TeXDict begin 29 28 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(29)3297 459 y Fe(\003)386 638 y Fg(R)-5 b(emark)35 b Fp(5.3)p Fg(.)e Fp(In)22 b(the)h(case)g(of)e(\(2.9\))g(w)m (e)i(de\014ne)h(\000)e(as)g(follo)m(ws:)39 b(W)-8 b(e)22 b(pic)m(k)h Fo(l)30 b Fk(\024)e Fo(n)p Fk(\000)p Fp(1)386 755 y(suc)m(h)34 b(that)e(\(2.9\))g(holds)i(and)e(write)1101 948 y Fo(\015)1152 963 y Fj(1)1219 948 y Fp(=)27 b Fo(c)1364 963 y Fm(l)1424 881 y Fo(x)p 1400 925 103 4 v 1406 1016 a Fp(~)-55 b Fo(x)1455 1031 y Fm(n)1535 948 y Fk(\001)21 b Fo(!)1645 963 y Fm(l)1671 948 y Fp(\()p Fo(E)1781 963 y Fj(0)1821 948 y Fp(\))h(+)g Fo(r)2023 963 y Fm(t;E)2128 948 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\);)1101 1143 y Fo(c)1143 1158 y Fm(l)1197 1143 y Fp(=)27 b Fo(@)1351 1158 y Fm(u)1392 1170 y Ff(l)1421 1143 y Fo(\015)1472 1158 y Fj(1)1511 1143 y Fp(\()p Fo(w)s(;)17 b(E)1738 1158 y Fj(0)1777 1143 y Fp(\))1815 1172 y Fn(j)p Fm(w)r Fj(=0)1981 1143 y Fo(;)120 b Fp(~)-55 b Fo(x)2177 1158 y Fm(n)2252 1143 y Fp(=)28 b Fo(tk)s Fp(\()p Fo(E)2555 1158 y Fj(0)2595 1143 y Fp(\))p Fo(:)386 1322 y Fp(The)44 b(op)s(erator)e Fo(G)j Fp(=)g Fo(G)1320 1337 y Fm(t)1394 1322 y Fp(=)g Fo(\015)1571 1286 y Fm(w)1566 1346 y(t)1628 1322 y Fp(\()p Fo(x;)17 b(p)p Fp(\))43 b(is)g(giv)m(en)h(b)m(y)g(the)f (sym)m(b)s(ol)h(\(using)f(the)386 1438 y(substitution)34 b(\(5.1\)\))525 1605 y Fo(\015)576 1620 y Fm(t)606 1605 y Fp(\()o Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(\015)1015 1564 y Fj(1)1010 1630 y Fm(t)1055 1605 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h Fo(\015)1453 1564 y Fj(2)1448 1630 y Fm(t)1493 1605 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o(;)1383 b(\(5.21\))525 1765 y Fo(\015)581 1724 y Fj(1)576 1790 y Fm(t)621 1765 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(t)1009 1724 y Fn(\000)p Fj(1)1104 1765 y Fo(x)22 b Fk(\001)g Fo(!)1292 1780 y Fm(l)1318 1765 y Fp(\()p Fo(E)1428 1780 y Fj(0)1468 1765 y Fp(\))p Fo(;)525 1986 y(\015)581 1945 y Fj(2)576 2011 y Fm(t)621 1986 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)984 1919 y Fo(k)s Fp(\()p Fo(E)1148 1934 y Fj(0)1188 1919 y Fp(\))p 984 1963 242 4 v 1071 2055 a Fo(c)1113 2070 y Fm(l)1236 1846 y Fi(\022)1309 1986 y Fo(r)1353 2001 y Fm(t;E)1458 1986 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)1892 1892 y Fi(X)1800 2107 y Fj(2)p Fn(\024j)p Fm(\013)p Fn(j\024)p Fm(m)2092 2116 y Fh(0)2144 1986 y Fo(c)2186 2001 y Fm(\013)2235 1986 y Fo(\015)2291 1945 y Fm(\013)2341 1986 y Fp(\()p Fo(x;)c(\030)5 b Fp(\))2563 1846 y Fi(\023)2640 1963 y Fp(~)2640 1986 y(~)-53 b Fo(g)2683 2001 y Fj(1)2723 1905 y Fi(\000)2768 1986 y Fo(t)2803 1945 y Fn(\000)p Fj(1)2898 1986 y Fo(x)2953 1905 y Fi(\001)3002 1963 y Fp(~)3002 1986 y(~)h Fo(g)3046 2001 y Fj(2)3085 1986 y Fp(\()p Fo(\030)5 b Fp(\))o Fo(;)386 2267 y Fp(cf.)53 b(\(5.2\).)f(One)36 b(pro)m(v)m(es)h(Prop)s(osition)f (5.1)f(with)h(this)h Fo(G)e Fp(in)h(the)g(same)h(w)m(a)m(y)f(as)386 2383 y(b)s(efore.)44 b(Let)32 b(\000)c(=)f(Re)17 b(\()p Fo(G)p Fp(\).)43 b(W)-8 b(e)33 b(ha)m(v)m(e)h(\(5.20\))e(for)g(this)h (\000.)1268 2607 y(6.)49 b Fq(Mourre)37 b(theor)-7 b(y)38 b(f)n(or)g Fp(\000)486 2781 y(Let)g(\000)g(b)s(e)h(as)f(in)h(Section)g (5)f(\(assuming)i(\014rst)f(\(2.8\)\).)60 b(The)39 b Fo(m)2875 2796 y Fj(0)2953 2781 y Fp(of)f(\(5.2\))g(is)386 2897 y(here)43 b(considered)g(as)f(arbitrary)g(\(but)g(\014xed\);)48 b(the)42 b(condition)h(\(5.3\))e(\(needed)386 3014 y(b)s(efore)33 b(for)f(dynamical)h(statemen)m(ts\))i(is)e(not)f(imp)s(osed.)486 3130 y(W)-8 b(e)33 b(in)m(tro)s(duce)g(for)f(0)c Fo(<)1421 3104 y Fp(\026)1416 3130 y Fo(\016)k Fk(\024)c Fp(1)k(the)h(op)s (erators)473 3279 y(\026)447 3304 y Fo(H)j Fp(=)27 b Fo(t)702 3263 y Fj(1)p Fn(\000)795 3246 y Fj(\026)792 3263 y Fm(\016)830 3304 y Fp(\000)p Fo(;)1058 3279 y Fp(\026)1033 3304 y Fo(A)g Fp(=)i(\026)-50 b Fo(a)1288 3263 y Fm(w)1288 3329 y(t)1345 3304 y Fp(\()p Fo(x;)17 b(p)p Fp(\);)1578 b(\(6.1\))449 3477 y(\026)-51 b Fo(a)498 3492 y Fm(t)528 3477 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(t)920 3419 y Fj(\026)917 3436 y Fm(\016)s Fn(\000)p Fj(1)1045 3397 y Fi(\000)1091 3477 y Fo(x)22 b Fk(\001)g Fo(!)1279 3492 y Fm(l)1305 3477 y Fp(\()p Fo(E)1415 3492 y Fj(0)1455 3477 y Fp(\))g(+)g Fo(x)g Fk(\001)1740 3397 y Fi(\000)1786 3477 y Fo(!)1847 3492 y Fm(l)1872 3477 y Fp(\()p Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))22 b Fk(\000)h Fo(!)2410 3492 y Fm(l)2435 3477 y Fp(\()p Fo(E)2545 3492 y Fj(0)2585 3477 y Fp(\))2623 3397 y Fi(\001)2672 3454 y Fp(~)2672 3477 y(~)-52 b Fo(g)2716 3492 y Fj(1)2755 3397 y Fi(\000)2800 3477 y Fo(t)2835 3436 y Fn(\000)p Fj(1)2930 3477 y Fo(x)2985 3397 y Fi(\001)3034 3454 y Fp(~)3034 3477 y(~)g Fo(g)3078 3492 y Fj(2)3117 3477 y Fp(\()p Fo(\030)5 b Fp(\))3240 3397 y Fi(\001)3286 3477 y Fo(:)486 3664 y Fp(W)-8 b(e)39 b(shall)h(need)g(a)f(sp)s (eci\014c)h(construction)h(of)d(the)i(functions)2850 3641 y(~)2850 3664 y(~)-52 b Fo(g)2894 3679 y Fj(1)2972 3664 y Fp(and)3172 3641 y(~)3172 3664 y(~)f Fo(g)3215 3679 y Fj(2)3293 3664 y Fp(in)386 3780 y(the)33 b(de\014nition)g(of) 1124 3755 y(\026)1099 3780 y Fo(H)40 b Fp(and)1435 3755 y(\026)1409 3780 y Fo(A)33 b Fp(ab)s(o)m(v)m(e)g(in)g(terms)h(of)e(a)g (small)h(parameter)g Fo(\017)28 b(>)g Fp(0:)486 3897 y(The)33 b(factor)969 3874 y(~)969 3897 y(~)-53 b Fo(g)1012 3912 y Fj(1)1051 3897 y Fp(\()p Fo(t)1124 3861 y Fn(\000)p Fj(1)1219 3897 y Fo(x)p Fp(\))33 b(is)g(the)g(pro)s(duct)g(of)f(the)h Fo(n)f Fp(functions)987 4065 y Fo(F)1050 4080 y Fn(\000)1110 3984 y Fi(\000)1155 4065 y Fo(\017)1194 4024 y Fn(\000)p Fj(3)1289 4065 y Fk(j)p Fo(t)1352 4024 y Fn(\000)p Fj(1)1446 4065 y Fo(x)23 b Fk(\001)f Fo(!)1635 4080 y Fm(j)1671 4065 y Fp(\()p Fo(E)1781 4080 y Fj(0)1820 4065 y Fp(\))p Fk(j)1886 3984 y Fi(\001)1932 4065 y Fp(;)114 b Fo(j)34 b Fp(=)27 b(1)p Fo(;)17 b(:)g(:)g(:)f(;)h(n)22 b Fk(\000)g Fp(1)p Fo(;)987 4226 y(F)1050 4241 y Fn(\000)1110 4145 y Fi(\000)1155 4226 y Fo(\017)1194 4185 y Fn(\000)p Fj(2)1289 4226 y Fk(j)p Fo(t)1352 4185 y Fn(\000)p Fj(1)1446 4226 y Fo(x)h Fk(\001)f Fo(!)1635 4241 y Fm(n)1681 4226 y Fp(\()p Fo(E)1791 4241 y Fj(0)1831 4226 y Fp(\))g Fk(\000)h Fo(k)s Fp(\()p Fo(E)2155 4241 y Fj(0)2194 4226 y Fp(\))p Fk(j)2260 4145 y Fi(\001)2305 4226 y Fo(:)3174 4147 y Fp(\(6.2\))486 4412 y(The)33 b(factor)969 4389 y(~)969 4412 y(~)-53 b Fo(g)1012 4427 y Fj(2)1051 4412 y Fp(\()p Fo(\030)5 b Fp(\))32 b(is)h(the)g(pro)s(duct)g(of)f(the)h Fo(n)g Fp(functions)565 4580 y Fo(F)628 4595 y Fn(\000)687 4500 y Fi(\000)733 4580 y Fo(\017)772 4539 y Fn(\000)p Fj(2)866 4580 y Fk(j)p Fp(\()p Fo(\030)27 b Fk(\000)22 b Fo(\030)5 b Fp(\()o Fo(E)1258 4595 y Fj(0)1298 4580 y Fp(\)\))22 b Fk(\001)g Fo(!)1507 4595 y Fm(l)1533 4580 y Fp(\()p Fo(E)1643 4595 y Fj(0)1682 4580 y Fp(\))p Fk(j)1748 4500 y Fi(\001)1794 4580 y Fo(;)565 4741 y(F)628 4756 y Fn(\000)687 4661 y Fi(\000)733 4741 y Fo(\017)772 4700 y Fn(\000)p Fj(3)866 4741 y Fk(j)p Fp(\()p Fo(\030)27 b Fk(\000)22 b Fo(\030)5 b Fp(\()o Fo(E)1258 4756 y Fj(0)1298 4741 y Fp(\)\))22 b Fk(\001)g Fo(!)1507 4756 y Fm(j)1543 4741 y Fp(\()p Fo(E)1653 4756 y Fj(0)1693 4741 y Fp(\))p Fk(j)1759 4661 y Fi(\001)1804 4741 y Fp(;)114 b Fo(j)34 b Fp(=)28 b(1)p Fo(;)17 b(:)g(:)g(:)e(;)i(n)22 b Fk(\000)h Fp(1)p Fo(;)114 b(j)33 b Fk(6)p Fp(=)28 b Fo(l)r(;)565 4902 y(F)628 4917 y Fn(\000)687 4822 y Fi(\000)733 4902 y Fo(\017)772 4861 y Fn(\000)p Fj(4)866 4902 y Fk(j)p Fp(\()p Fo(\030)f Fk(\000)22 b Fo(\030)5 b Fp(\()o Fo(E)1258 4917 y Fj(0)1298 4902 y Fp(\)\))22 b Fk(\001)g Fo(!)1507 4917 y Fm(n)1554 4902 y Fp(\()p Fo(E)1664 4917 y Fj(0)1703 4902 y Fp(\))p Fk(j)1769 4822 y Fi(\001)1815 4902 y Fo(:)3174 4743 y Fp(\(6.3\))486 5108 y(W)-8 b(e)33 b(ha)m(v)m(e)g(the)g(follo)m (wing)g(result)h(\(with)1990 5027 y Fi(\012)2063 5083 y Fp(\026)2037 5108 y Fo(A)2110 5027 y Fi(\013)2185 5108 y Fp(=)2288 5027 y Fi(\000)2334 5108 y Fp(1)22 b(+)2529 5083 y(\026)2503 5108 y Fo(A)2576 5072 y Fj(2)2616 5027 y Fi(\001)2661 5049 y Fj(1)p Fm(=)p Fj(2)2804 5108 y Fp(\).)386 5287 y FC(Lemma)36 b(6.1.)k Fg(Ther)-5 b(e)32 b(exists)g Fo(\017)1575 5302 y Fj(0)1643 5287 y Fo(>)27 b Fp(0)32 b Fg(such)h(that)g(for)f(al)5 b(l)32 b(p)-5 b(ositive)32 b Fo(\017)c Fk(\024)g Fo(\017)3094 5302 y Fj(0)3167 5287 y Fg(ther)-5 b(e)386 5404 y(exist)35 b(c)-5 b(onstants)34 b Fo(t)1076 5419 y Fj(0)1116 5404 y Fo(;)17 b(C)34 b(>)27 b Fp(1)35 b Fg(such)g(that)g(for)g(al)5 b(l)34 b Fo(t)28 b Fk(\025)g Fo(t)2370 5419 y Fj(0)2445 5404 y Fg(and)34 b Fo(h)28 b Fk(2)g Fo(C)2889 5367 y Fn(1)2882 5428 y Fj(0)2964 5404 y Fp(\()p FC(R)p Fp(\))1200 5503 y Fi(\015)1200 5563 y(\015)1256 5507 y(\012)1328 5563 y Fp(\026)1303 5588 y Fo(A)1376 5507 y Fi(\013)1423 5529 y Fn(\000)p Fj(1)1517 5588 y Fo(h)1573 5507 y Fi(\000)1644 5563 y Fp(\026)1619 5588 y Fo(H)1707 5507 y Fi(\001\012)1826 5563 y Fp(\026)1800 5588 y Fo(A)1873 5507 y Fi(\013)1920 5529 y Fn(\000)p Fj(1)2015 5503 y Fi(\015)2015 5563 y(\015)2098 5588 y Fk(\024)g Fo(C)7 b Fk(jj)p Fo(h)p Fk(jj)2448 5605 y Fm(L)2496 5586 y Fh(1)2533 5588 y Fo(:)614 b Fp(\(6.4\))p eop end %%Page: 30 30 TeXDict begin 30 29 bop 386 259 a Fl(30)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y Fg(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)35 b(shall)f(use)h(the)g(abstract)g(theory)f(of)g([M])h (with)f(the)h(conjugate)f(op-)386 575 y(erator)699 550 y(\026)673 575 y Fo(A)f Fp(to)f(obtain)h(a)f(globally)h(uniform)f (resolv)m(en)m(t)j(b)s(ound.)486 691 y(W)-8 b(e)33 b(claim)g(that)f (for)g(all)h(small)g(enough)g Fo(\017)1215 864 y(i)1248 783 y Fi(\002)1315 839 y Fp(\026)1290 864 y Fo(H)8 b(;)1448 839 y Fp(\026)1423 864 y Fo(A)1496 783 y Fi(\003)1565 864 y Fk(\025)28 b Fp(2)1719 823 y Fn(\000)p Fj(1)1813 864 y Fp(;)114 b Fo(t)28 b Fk(\025)g Fo(t)2157 879 y Fj(0)2225 864 y Fp(=)f Fo(t)2363 879 y Fj(0)2403 864 y Fp(\()p Fo(\017)p Fp(\))p Fo(:)629 b Fp(\(6.5\))486 1038 y(T)-8 b(o)30 b(see)h(this)g(w)m(e)h(notice)f(that)f(clearly)h (the)g(\014rst)g(term)g(in)f(\(5.2\))g(and)g(the)h(\014rst)386 1154 y(term)i(of)f(the)h(sym)m(b)s(ol)i(\026)-50 b Fo(a)33 b Fp(con)m(tribute)g(b)m(y)1093 1353 y Fo(i)1126 1242 y Fi(h)1174 1353 y Fo(t)1209 1311 y Fj(1)p Fn(\000)1302 1294 y Fj(\026)1299 1311 y Fm(\016)1337 1272 y Fi(\000)1383 1353 y Fo(\015)1439 1311 y Fj(1)1478 1272 y Fi(\001)1524 1294 y Fm(w)1580 1353 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(;)g(t)1886 1294 y Fj(\026)1883 1311 y Fm(\016)s Fn(\000)p Fj(1)2011 1353 y Fo(x)23 b Fk(\001)f Fo(!)2200 1368 y Fm(l)2225 1353 y Fp(\()p Fo(E)2335 1368 y Fj(0)2375 1353 y Fp(\))2413 1242 y Fi(i)2488 1353 y Fp(=)27 b(1)p Fo(;)386 1548 y Fp(so)33 b(it)f(remains)i(to)e(estimate)933 1613 y Fi(\015)933 1672 y(\015)933 1732 y(\015)988 1727 y Fo(i)1021 1617 y Fi(h)1068 1727 y Fo(t)1103 1686 y Fj(1)p Fn(\000)1196 1669 y Fj(\026)1193 1686 y Fm(\016)1231 1647 y Fi(\000)1277 1727 y Fp(Re)1409 1647 y Fi(\000)1455 1727 y Fo(\015)1511 1686 y Fj(2)1506 1752 y Fm(t)1550 1647 y Fi(\001\001)1641 1669 y Fm(w)1698 1727 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(;)1991 1702 y Fp(\026)1966 1727 y Fo(A)2039 1617 y Fi(i)2086 1613 y(\015)2086 1672 y(\015)2086 1732 y(\015)2169 1727 y Fk(\024)28 b Fp(4)2323 1686 y Fn(\000)p Fj(1)2417 1727 y Fp(;)114 b Fo(t)28 b Fk(\025)g Fo(t)2761 1742 y Fj(0)2801 1727 y Fo(;)346 b Fp(\(6.6\))386 1926 y(and)600 1990 y Fi(\015)600 2050 y(\015)600 2110 y(\015)656 2105 y Fo(i)689 1994 y Fi(h)736 2105 y Fo(t)771 2064 y Fj(1)p Fn(\000)864 2046 y Fj(\026)861 2064 y Fm(\016)899 2024 y Fi(\000)945 2105 y Fo(\015)1001 2064 y Fj(1)1041 2024 y Fi(\001)1086 2047 y Fm(w)1143 2105 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fo(;)1436 2080 y Fp(\026)1411 2105 y Fo(A)22 b Fk(\000)g Fo(t)1643 2046 y Fj(\026)1640 2064 y Fm(\016)s Fn(\000)p Fj(1)1769 2105 y Fo(x)g Fk(\001)g Fo(!)1957 2120 y Fm(l)1983 2105 y Fp(\()p Fo(E)2093 2120 y Fj(0)2132 2105 y Fp(\))2170 1994 y Fi(i)2217 1990 y(\015)2217 2050 y(\015)2217 2110 y(\015)2300 2105 y Fk(\024)28 b Fp(4)2454 2064 y Fn(\000)p Fj(1)2549 2105 y Fp(;)114 b Fo(t)28 b Fk(\025)g Fo(t)2893 2120 y Fj(0)2933 2105 y Fo(:)214 b Fp(\(6.7\))486 2309 y(Let)38 b(us)h(denote)g(b)m(y)g Fo(a)1309 2324 y Fm(t)1339 2309 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))38 b(the)h(W)-8 b(eyl)39 b(sym)m(b)s(ol)g(of)f(the)h(op)s(erator)f(in)g(\(6.6\))386 2432 y(or)43 b(the)g(one)h(in)f(\(6.7\).)75 b(W)-8 b(e)43 b(ha)m(v)m(e)i(in)e(b)s(oth)g(cases)i(that)e Fo(a)2619 2447 y Fm(t)2694 2432 y Fk(2)j Fo(S)2866 2447 y Fm(unif)3019 2352 y Fi(\000)3065 2432 y Fp(1)p Fo(;)17 b(g)3209 2385 y Fj(1)p Fm(;)p Fj(0)3205 2455 y Fm(t)3302 2352 y Fi(\001)3348 2432 y Fp(,)386 2550 y(so)35 b(it)g(su\016ces)j(to)c(sho)m(w)j(\(cf.)51 b([H\177)-49 b(o,)36 b(Theorem)g(18.6.3])f(and)g(the)h(pro)s(of)e(of)g ([DG,)386 2666 y(Prop)s(osition)f(D.5.1]\))f(that)1495 2839 y(sup)1367 2921 y Fm(x;\030)s Fn(2)p Fd(R)1569 2902 y Ff(n)1611 2921 y Fm(;t)p Fn(\025)p Fm(t)1736 2930 y Fh(0)1787 2839 y Fk(j)p Fo(a)1866 2854 y Fm(t)1896 2839 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fk(j)27 b(\024)i Fo(\027)2327 2854 y Fj(0)2366 2839 y Fo(;)781 b Fp(\(6.8\))386 3083 y(where)28 b Fo(\027)710 3098 y Fj(0)777 3083 y Fp(is)g(a)f(\(univ)m(ersal\))i(small)f(p)s(ositiv)m(e)g(constan)m(t)g (asso)s(ciated)g(for)f(example)386 3199 y(to)32 b(the)h Fo(L)739 3163 y Fj(2)811 3199 y Fp({b)s(oundedness)i(result)f([H\177) -49 b(o,)32 b(Theorem)i(18.6.3].)486 3316 y(F)-8 b(or)31 b(\(6.8\))h(w)m(e)i(note)f(the)g(uniform)g(b)s(ounds)583 3490 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)h Fo(E)1056 3505 y Fj(0)1123 3490 y Fp(=)28 b Fo(O)1305 3409 y Fi(\000)1349 3490 y Fo(\017)1388 3449 y Fj(4)1428 3409 y Fi(\001)1474 3490 y Fo(;)583 3651 y(t@)669 3666 y Fm(x)709 3676 y Ff(j)746 3651 y Fo(h)p Fp(\()q Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(O)1234 3570 y Fi(\000)1279 3651 y Fo(\017)1318 3610 y Fj(2)1358 3570 y Fi(\001)1404 3651 y Fo(;)583 3812 y(@)634 3827 y Fm(\030)665 3837 y Ff(j)703 3812 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(O)1190 3731 y Fi(\000)1235 3812 y Fo(\017)1274 3771 y Fj(2)1314 3731 y Fi(\001)1392 3812 y Fp(for)32 b Fo(j)i Fk(\024)28 b Fo(n)22 b Fk(\000)h Fp(1)p Fo(;)114 b(@)2141 3827 y Fm(\030)2172 3835 y Ff(n)2219 3812 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(O)2707 3731 y Fi(\000)2752 3812 y Fo(\017)2791 3771 y Fj(0)2831 3731 y Fi(\001)2876 3812 y Fo(;)583 3973 y(\015)634 3988 y Fm(j)670 3973 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(O)1102 3892 y Fi(\000)1147 3973 y Fo(\017)1186 3932 y Fj(2)1226 3892 y Fi(\001)1271 3973 y Fo(;)115 b(t@)1499 3988 y Fm(x)1543 3973 y Fo(\015)1594 3988 y Fm(j)1630 3973 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(O)2062 3892 y Fi(\000)2107 3973 y Fo(\017)2146 3932 y Fj(0)2186 3892 y Fi(\001)2232 3973 y Fo(;)114 b(@)2424 3988 y Fm(\030)2462 3973 y Fo(\015)2513 3988 y Fm(j)2549 3973 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(O)2981 3892 y Fi(\000)3026 3973 y Fo(\017)3065 3932 y Fj(0)3105 3892 y Fi(\001)3150 3973 y Fo(;)386 4166 y Fp(on)35 b(the)i(supp)s(ort)f(of)f(the)h(function)1733 4143 y(~)1733 4166 y(~)-52 b Fo(g)1777 4181 y Fj(1)1816 4166 y Fp(\()p Fo(t)1889 4130 y Fn(\000)p Fj(1)1984 4166 y Fo(x)p Fp(\))2080 4143 y(~)2080 4166 y(~)g Fo(g)2124 4181 y Fj(2)2163 4166 y Fp(\()p Fo(\030)5 b Fp(\))35 b(giv)m(en)i(b)m(y)f(\(6.2\))f(and)h(\(6.3\).)386 4282 y(Here)d(w)m(e)h(used)g(\(1.3\))e(and)g(\(1.4\),)g(and)h(the)g (notation)1171 4455 y Fo(x)1226 4470 y Fm(j)1291 4455 y Fp(=)27 b Fo(x)c Fk(\001)f Fo(!)1583 4470 y Fm(j)1619 4455 y Fp(\()p Fo(E)1729 4470 y Fj(0)1769 4455 y Fp(\))p Fo(;)114 b(\030)1991 4470 y Fm(j)2055 4455 y Fp(=)27 b Fo(\030)g Fk(\001)22 b Fo(!)2339 4470 y Fm(j)2375 4455 y Fp(\()p Fo(E)2485 4470 y Fj(0)2524 4455 y Fp(\))p Fo(:)486 4627 y Fp(By)28 b(estimating)i(the)e(leading)h(term)g(of)f(the)g(sym)m (b)s(ol)i(using)f(these)h(b)s(ounds)f(w)m(e)386 4743 y(ma)m(y)k(sho)m(w)h(\(with)f(some)h(patience\))f(that)1481 4916 y(sup)1353 4998 y Fm(x;\030)s Fn(2)p Fd(R)1555 4979 y Ff(n)1596 4998 y Fm(;t)p Fn(\025)p Fm(t)1721 5007 y Fh(0)1773 4916 y Fk(j)p Fo(a)1852 4931 y Fm(t)1881 4916 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)7 b(\017;)767 b Fp(\(6.9\))386 5160 y(from)32 b(whic)m(h)i (\(6.8\))e(and)h(\(therefore\))g(\(6.5\))f(follo)m(w.)486 5276 y(As)22 b(for)f(the)h(b)s(oundedness)i(of)d(second)i(comm)m (utators)g(required)g(b)m(y)g(the)f(Mourre)386 5393 y(theory)33 b(w)m(e)h(ha)m(v)m(e)g(the)f(b)s(ound)1122 5506 y Fi(\015)1122 5566 y(\015)1177 5591 y Fo(i)1210 5510 y Fi(\002)1252 5591 y Fo(i)1285 5510 y Fi(\002)1352 5566 y Fp(\026)1327 5591 y Fo(H)8 b(;)1485 5566 y Fp(\026)1460 5591 y Fo(A)1532 5510 y Fi(\003)1574 5591 y Fo(;)1643 5566 y Fp(\026)1618 5591 y Fo(A)1691 5510 y Fi(\003)1732 5506 y(\015)1732 5566 y(\015)1815 5591 y Fp(=)28 b Fo(O)1997 5481 y Fi(\020)2056 5591 y Fo(t)2094 5532 y Fj(\026)2091 5550 y Fm(\016)r Fn(\000)p Fj(1)2219 5481 y Fi(\021)2306 5591 y Fp(=)g Fo(O)s Fp(\()o(1\))o Fo(:)487 b Fp(\(6.10\))p eop end %%Page: 31 31 TeXDict begin 31 30 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(31)486 459 y Fp(Using)23 b(\(6.5\))f(and)h(\(6.10\))f (w)m(e)i(readily)g(obtain)f(b)m(y)h(k)m(eeping)g(trac)m(k)g(of)e (constan)m(ts)386 575 y(in)33 b(the)g(metho)s(d)g(of)f([M])h(that)f (for)g(some)i(p)s(ositiv)m(e)g(constan)m(t)f Fo(C)653 649 y Fi(\015)653 709 y(\015)653 768 y(\015)709 683 y(\012)782 738 y Fp(\026)756 763 y Fo(A)829 683 y Fi(\013)876 705 y Fn(\000)p Fj(1)970 683 y Fi(\000)1041 738 y Fp(\026)1016 763 y Fo(H)d Fk(\000)22 b Fo(z)1275 683 y Fi(\001)1322 705 y Fn(\000)p Fj(1)1416 683 y Fi(\012)1489 738 y Fp(\026)1463 763 y Fo(A)1536 683 y Fi(\013)1583 705 y Fn(\000)p Fj(1)1678 649 y Fi(\015)1678 709 y(\015)1678 768 y(\015)1761 763 y Fk(\024)28 b Fo(C)7 b Fp(;)114 b(Im)17 b Fo(z)32 b Fk(6)p Fp(=)c(0)p Fo(;)114 b(t)28 b Fk(\025)g Fo(t)2791 778 y Fj(0)2831 763 y Fo(:)267 b Fp(\(6.11\))486 978 y(Represen)m(ting)44 b Fo(h)1136 898 y Fi(\000)1207 953 y Fp(\026)1182 978 y Fo(H)1270 898 y Fi(\001)1361 978 y Fp(=)h Fo(\031)1541 942 y Fn(\000)p Fj(1)1652 978 y Fp(lim)1787 993 y Fm(\017)p Fn(#)p Fj(0)1907 898 y Fi(R)1990 978 y Fo(h)p Fp(\()p Fo(\025)p Fp(\))17 b(Im)2329 898 y Fi(\000)o(\000)2445 953 y Fp(\026)2420 978 y Fo(H)30 b Fk(\000)22 b Fo(\025)g Fk(\000)h Fo(i\017)2881 898 y Fi(\001)2927 920 y Fn(\000)p Fj(1)3022 898 y Fi(\001)3067 978 y Fo(d\025)43 b Fp(and)386 1096 y(then)33 b(using)g(\(6.11\))f(w)m (e)i(conclude)g(\(6.4\).)1379 b Fe(\003)386 1258 y Fg(R)-5 b(emark.)37 b Fp(Although)29 b(stated)g(for)e(concrete)j(op)s(erators) 2473 1233 y(\026)2448 1258 y Fo(H)35 b Fp(and)2775 1233 y(\026)2749 1258 y Fo(A)29 b Fp(clearly)g(there)386 1375 y(is)f(an)g(abstract)g(v)m(ersion)i(of)d(Lemma)i(6.1;)g(the)f(imp)s (ortan)m(t)g(prop)s(erties)h(are)f(\(6.5\))386 1491 y(and)33 b(\(6.10\).)386 1653 y FC(Corollary)46 b(6.2.)e Fg(Supp)-5 b(ose)40 b Fo(h)1543 1668 y Fj(1)1582 1653 y Fo(;)17 b(h)1682 1668 y Fj(2)1759 1653 y Fk(2)37 b Fo(C)1939 1617 y Fn(1)1932 1678 y Fj(0)2014 1653 y Fp(\()p FC(R)p Fp(\))j Fg(and)f Fp(0)e Fk(\024)h Fo(\033)j(<)2822 1627 y Fp(\026)2818 1653 y Fo(\016)g Fk(\024)d Fp(1)p Fg(.)60 b(Then)386 1769 y(ther)-5 b(e)38 b(exists)f Fo(\017)940 1784 y Fj(0)1013 1769 y Fo(>)c Fp(0)38 b Fg(such)g(that)g(for)g(al)5 b(l)37 b(p)-5 b(ositive)37 b Fo(\017)d Fk(\024)g Fo(\017)2514 1784 y Fj(0)2591 1769 y Fg(ther)-5 b(e)38 b(exists)g Fo(C)i(>)33 b Fp(0)386 1885 y Fg(such)i(that)g(for)g(al)5 b(l)34 b Fo(t)28 b Fk(\025)g Fp(1)1181 1954 y Fi(\015)1181 2014 y(\015)1181 2073 y(\015)1236 2068 y Fo(h)1292 2083 y Fj(1)1332 1988 y Fi(\000)1403 2043 y Fp(\026)1378 2068 y Fo(A)1451 1988 y Fi(\001)1496 2068 y Fo(h)1552 2083 y Fj(2)1592 1958 y Fi(\020)1652 2068 y Fo(t)1690 2010 y Fj(\026)1687 2027 y Fm(\016)r Fn(\000)p Fm(\033)1848 2043 y Fp(\026)1822 2068 y Fo(H)1911 1958 y Fi(\021)1970 1954 y(\015)1970 2014 y(\015)1970 2073 y(\015)2053 2068 y Fk(\024)g Fo(C)7 b(t)2270 2033 y Fp(\()2309 2024 y Fm(\033)r Fn(\000)2409 2007 y Fj(\026)2406 2024 y Fm(\016)2440 2032 y Fp(\))2478 2024 y Fm(=)p Fj(2)2552 2068 y Fo(:)546 b Fp(\(6.12\))386 2262 y Fg(R)-5 b(emark)51 b Fp(6.3)p Fg(.)44 b Fp(In)c(the)f(case)h(of)f(\(2.9\))f(w)m(e)j(in)m(tro)s(duce)f (\(with)f(\000)g(as)h(in)f(Remark)386 2378 y(5.3\))514 2524 y(\026)489 2549 y Fo(H)c Fp(=)28 b Fo(t)744 2508 y Fj(1)p Fn(\000)837 2490 y Fj(\026)834 2508 y Fm(\016)872 2549 y Fp(\000)p Fo(;)1100 2524 y Fp(\026)1074 2549 y Fo(A)g Fp(=)h(\026)-50 b Fo(a)1330 2508 y Fm(w)1330 2574 y(t)1386 2549 y Fp(\()p Fo(x;)17 b(p)p Fp(\);)490 2722 y(\026)-50 b Fo(a)540 2737 y Fm(t)570 2722 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(t)961 2663 y Fj(\026)958 2681 y Fm(\016)997 2641 y Fi(\000)1042 2722 y Fp(\()p Fo(p)22 b Fk(\000)h Fo(\030)5 b Fp(\()o Fo(E)1408 2737 y Fj(0)1448 2722 y Fp(\)\))22 b Fk(\001)g Fo(!)1657 2737 y Fm(l)1682 2722 y Fp(\()p Fo(E)1792 2737 y Fj(0)1832 2722 y Fp(\))g(+)g Fo(b)p Fp(\()q Fo(x;)17 b(\030)5 b Fp(\))2258 2699 y(~)2258 2722 y(~)-53 b Fo(g)2301 2737 y Fj(1)2340 2641 y Fi(\000)2386 2722 y Fo(t)2421 2681 y Fn(\000)p Fj(1)2515 2722 y Fo(x)2570 2641 y Fi(\001)2620 2699 y Fp(~)2620 2722 y(~)g Fo(g)2663 2737 y Fj(2)2703 2722 y Fp(\()p Fo(\030)5 b Fp(\))2826 2641 y Fi(\001)2872 2722 y Fo(;)489 2873 y(b)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f(\()p Fo(p)22 b Fk(\000)h Fo(\030)5 b Fp(\()o Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\)\))22 b Fk(\001)g Fo(!)1666 2888 y Fm(l)1691 2873 y Fp(\()p Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))22 b Fk(\000)g Fp(\()p Fo(p)h Fk(\000)f Fo(\030)5 b Fp(\()p Fo(E)2534 2888 y Fj(0)2573 2873 y Fp(\)\))22 b Fk(\001)g Fo(!)2782 2888 y Fm(l)2808 2873 y Fp(\()p Fo(E)2918 2888 y Fj(0)2957 2873 y Fp(\))p Fo(:)3125 2707 y Fp(\(6.13\))386 3051 y(Here)33 b(the)g(factor)1067 3027 y(~)1067 3051 y(~)-53 b Fo(g)1110 3066 y Fj(1)1149 3051 y Fp(\()p Fo(t)1222 3014 y Fn(\000)p Fj(1)1317 3051 y Fo(x)p Fp(\))33 b(is)g(the)g(pro)s (duct)g(of)f(the)h Fo(n)g Fp(functions)803 3209 y Fo(F)866 3224 y Fn(\000)926 3128 y Fi(\000)971 3209 y Fo(\017)1010 3168 y Fn(\000)p Fj(2)1105 3209 y Fk(j)p Fo(t)1168 3168 y Fn(\000)p Fj(1)1262 3209 y Fo(x)23 b Fk(\001)f Fo(!)1451 3224 y Fm(l)1476 3209 y Fp(\()p Fo(E)1586 3224 y Fj(0)1626 3209 y Fp(\))p Fk(j)1692 3128 y Fi(\001)1737 3209 y Fo(;)803 3370 y(F)866 3385 y Fn(\000)926 3289 y Fi(\000)971 3370 y Fo(\017)1010 3329 y Fn(\000)p Fj(3)1105 3370 y Fk(j)p Fo(t)1168 3329 y Fn(\000)p Fj(1)1262 3370 y Fo(x)h Fk(\001)f Fo(!)1451 3385 y Fm(j)1487 3370 y Fp(\()p Fo(E)1597 3385 y Fj(0)1636 3370 y Fp(\))p Fk(j)1702 3289 y Fi(\001)1748 3370 y Fp(;)114 b Fo(j)34 b Fp(=)27 b(1)p Fo(;)17 b Fk(\001)g(\001)g (\001)31 b Fo(;)17 b(n)22 b Fk(\000)h Fp(1)p Fo(;)114 b(j)33 b Fk(6)p Fp(=)28 b Fo(l)r(;)803 3531 y(F)866 3546 y Fn(\000)926 3451 y Fi(\000)971 3531 y Fo(\017)1010 3490 y Fn(\000)p Fj(2)1105 3531 y Fk(j)p Fo(t)1168 3490 y Fn(\000)p Fj(1)1262 3531 y Fo(x)23 b Fk(\001)f Fo(!)1451 3546 y Fm(n)1497 3531 y Fp(\()p Fo(E)1607 3546 y Fj(0)1647 3531 y Fp(\))g Fk(\000)h Fo(k)s Fp(\()p Fo(E)1971 3546 y Fj(0)2010 3531 y Fp(\))p Fk(j)2076 3451 y Fi(\001)2121 3531 y Fo(;)386 3709 y Fp(while)34 b(the)f(factor)1091 3685 y(~)1091 3709 y(~)-52 b Fo(g)1135 3724 y Fj(2)1174 3709 y Fp(\()p Fo(\030)5 b Fp(\))32 b(is)h(the)g(pro)s(duct)g(of)831 3867 y Fo(F)894 3882 y Fn(\000)953 3786 y Fi(\000)999 3867 y Fo(\017)1038 3826 y Fn(\000)p Fj(3)1132 3867 y Fk(j)p Fp(\()p Fo(\030)26 b Fk(\000)d Fo(\030)5 b Fp(\()o Fo(E)1524 3882 y Fj(0)1564 3867 y Fp(\)\))22 b Fk(\001)g Fo(!)1773 3882 y Fm(j)1809 3867 y Fp(\()p Fo(E)1919 3882 y Fj(0)1959 3867 y Fp(\))p Fk(j)2025 3786 y Fi(\001)2070 3867 y Fp(;)114 b Fo(j)34 b Fp(=)27 b(1)p Fo(;)17 b Fk(\001)g(\001)g (\001)31 b Fo(;)17 b(n)22 b Fk(\000)h Fp(1)p Fo(;)831 4028 y(F)894 4043 y Fn(\000)953 3947 y Fi(\000)999 4028 y Fo(\017)1038 3987 y Fn(\000)p Fj(4)1132 4028 y Fk(j)p Fp(\()p Fo(\030)j Fk(\000)d Fo(\030)5 b Fp(\()o Fo(E)1524 4043 y Fj(0)1564 4028 y Fp(\)\))22 b Fk(\001)g Fo(!)1773 4043 y Fm(n)1820 4028 y Fp(\()p Fo(E)1930 4043 y Fj(0)1969 4028 y Fp(\))p Fk(j)2035 3947 y Fi(\001)2080 4028 y Fo(:)486 4196 y Fp(One)46 b(v)m(eri\014es)h(\(6.12\))e(under)i(the)f(same)h (conditions)f(as)g(in)g(Corollary)g(6.2)386 4312 y(along)32 b(the)h(same)g(line)h(as)f(b)s(efore.)1252 4510 y(7.)49 b Fq(Pr)n(oof)38 b(of)h(Theorem)e(1.1)486 4684 y Fp(The)30 b(pro)s(of)f(of)h(Theorem)h(1.1)e(is)i(based)f(on)g(Prop)s(osition)g (4.6,)g(and)g(Corollar-)386 4801 y(ies)j(5.2)g(and)f(6.2)g(\(with)i (the)f(assumption)g(\(2.8\)\).)486 4917 y(W)-8 b(e)34 b(recall)g(the)h(assumptions)h(of)d(Prop)s(osition)h(4.6:)46 b(0)30 b Fo(<)g Fp(2)p Fo(\016)k(<)29 b Fp(min)18 b(\()p Fo(\027)q(;)f Fp(2)p Fo(\016)3301 4881 y Fm(s)3337 4917 y Fp(\))386 5033 y(with)33 b Fo(\027)h(<)28 b Fp(2)p Fo(=)p Fp(5)k(and)g Fo(\016)1209 4997 y Fm(s)1279 5033 y Fp(as)g(in)h(\(2.14\).)386 5195 y FC(Lemma)k(7.1.)j Fg(With)1264 5170 y Fp(\026)1238 5195 y Fo(A)28 b Fp(=)1468 5170 y(\026)1442 5195 y Fo(A)1515 5210 y Fm(t)1578 5195 y Fg(given)33 b(in)g(terms)g(of)g(any)g(\(smal)5 b(l\))32 b Fo(\017)c(>)f Fp(0)33 b Fg(and)g(of)390 5285 y Fp(\026)386 5311 y Fo(\016)f Fp(=)c Fo(\016)39 b Fg(\(with)c Fo(\016)k Fg(as)c(ab)-5 b(ove\))34 b(by)h(either)g(\(6.1\))f(\(in)h(the)g(c)-5 b(ase)35 b(of)f(\(2.8\)\))h(or)g(\(6.13\))386 5428 y(\(in)f(the)h(c)-5 b(ase)34 b(of)h(\(2.9\)\))1385 5586 y Fp(lim)1370 5646 y Fm(t)p Fn(!1)1553 5586 y Fk(jj)p Fo(F)1672 5601 y Fj(+)1731 5505 y Fi(\000)1776 5586 y Fk(j)1830 5561 y Fp(\026)1804 5586 y Fo(A)p Fk(j)1905 5505 y Fi(\001)1950 5586 y Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)27 b Fp(=)h(0)p Fo(;)783 b Fp(\(7.1\))p eop end %%Page: 32 32 TeXDict begin 32 31 bop 386 259 a Fl(32)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y Fg(wher)-5 b(e)35 b Fo( )f Fp(=)c Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )40 b Fg(is)c(given)g(as)f(in)h(Pr)-5 b(op)g(osition)35 b(4.6)h(\(with)g Fo(f)47 b Fg(str)-5 b(ongly)36 b(sup-)386 575 y(p)-5 b(orte)g(d)35 b(dep)-5 b(ending)33 b(on)h Fo(\017)p Fg(\).)386 756 y(Pr)-5 b(o)g(of.)41 b Fp(W)-8 b(e)26 b(\014x)g Fo(\016)1019 771 y Fj(1)1084 756 y Fp(suc)m(h)h(that)f (2)p Fo(\016)31 b(<)d Fp(2)p Fo(\016)1821 771 y Fj(1)1888 756 y Fo(<)f Fp(min)18 b(\()p Fo(\027)q(;)f Fp(2)p Fo(\016)2398 720 y Fm(s)2434 756 y Fp(\).)41 b(Let)26 b Fo(b)2749 771 y Fm(t)2779 756 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))25 b(b)s(e)h(giv)m(en)386 872 y(b)m(y)33 b(\(4.14\))f(in)h(terms)h(of)e Fo(\016)1343 887 y Fj(1)1415 872 y Fp(and)g Fo(\027)6 b Fp(.)486 988 y(By)33 b(Prop)s(osition)f(4.6)h(it)f(su\016ces)j(to)d (sho)m(w)i(that)1142 1157 y Fk(jj)p Fo(F)1261 1172 y Fj(+)1319 1076 y Fi(\000)1365 1157 y Fk(j)1418 1132 y Fp(\026)1393 1157 y Fo(A)p Fk(j)1494 1076 y Fi(\001)1539 1157 y Fo(b)1580 1116 y Fm(w)1580 1182 y(t)1637 1157 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fk(jj)27 b(!)h Fp(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(;)386 1325 y Fp(and)33 b(therefore)g(in)g(turn) 1367 1494 y Fk(jj)1448 1469 y Fp(\026)1423 1494 y Fo(Ab)1537 1453 y Fm(w)1537 1519 y(t)1594 1494 y Fp(\()p Fo(x;)17 b(p)p Fp(\))p Fk(jj)27 b Fp(=)g Fo(O)2082 1413 y Fi(\000)2127 1494 y Fo(t)2162 1453 y Fm(\016)r Fn(\000)p Fm(\016)2281 1462 y Fh(1)2321 1413 y Fi(\001)2366 1494 y Fo(:)386 1671 y Fp(F)-8 b(or)45 b(the)i(latter)f(b)s(ound)g(one)h(easily)g(c)m (hec)m(k)i(that)d(the)g(sym)m(b)s(ol)i(of)3005 1646 y(\026)2980 1671 y Fo(Ab)3094 1635 y Fm(w)3094 1695 y(t)3151 1671 y Fp(\()p Fo(x;)17 b(p)p Fp(\))386 1787 y(b)s(elongs)33 b(to)1146 1941 y Fo(S)1206 1956 y Fm(unf)1335 1830 y Fi(\020)1394 1941 y Fo(t)1429 1900 y Fm(\016)r Fn(\000)p Fm(\016)1548 1909 y Fh(1)1588 1941 y Fo(;)17 b(g)1683 1894 y Fj(1)p Fn(\000)p Fm(\027)1812 1870 y Fc(0)1834 1894 y Fm(;\027)1893 1870 y Fc(0)1679 1963 y Fm(t)1919 1830 y Fi(\021)1978 1941 y Fp(;)115 b Fo(\027)2174 1900 y Fn(0)2225 1941 y Fp(=)28 b Fo(\027)g Fk(\000)23 b Fo(\016)2548 1956 y Fj(1)2588 1941 y Fo(:)3297 2113 y Fe(\003)486 2293 y Fp(No)m(w,)33 b(w)m(e)g(\014rst)g(\014x)h Fo(\016)i Fp(as)d(ab)s(o)m(v)m(e)g(and)g(conclude)h(from)e(Lemma)i(7.1)e(that) 1064 2462 y Fk(jj)p Fo( )t Fp(\()o Fo(t)p Fp(\))22 b Fk(\000)h Fo(F)1482 2477 y Fn(\000)1541 2381 y Fi(\000)1587 2462 y Fk(j)1640 2437 y Fp(\026)1615 2462 y Fo(A)p Fk(j)1716 2381 y Fi(\001)1761 2462 y Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)k(!)g Fp(0)33 b(for)f Fo(t)c Fk(!)f(1)p Fo(;)477 b Fp(\(7.2\))386 2632 y(where)39 b Fo( )i Fp(=)c Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )42 b Fp(is)d(giv)m(en)g(as)g(in)f(Prop)s (osition)g(4.6.)60 b(This)39 b(holds)g(for)f Fo(f)47 b Fk(2)386 2748 y Fo(C)463 2712 y Fn(1)456 2773 y Fj(0)538 2748 y Fp(\()p Fo(I)619 2763 y Fj(0)658 2748 y Fp(\);)33 b Fo(I)799 2763 y Fj(0)866 2748 y Fp(=)27 b Fo(I)1012 2763 y Fj(0)1052 2748 y Fp(\()p Fo(\017)p Fp(\).)486 2864 y(Next)42 b(w)m(e)g(\014x)g(an)m(y)g Fo(\033)k Fk(2)d Fp(\(0)p Fo(;)17 b(\016)t Fp(\))41 b(in)g(agreemen)m(t)i(with)f (Corollary)f(5.2)g(whic)m(h)386 2981 y(means)34 b(that)1134 3108 y Fk(jj)p Fo(F)1253 3123 y Fj(+)1311 3028 y Fi(\000)1357 3108 y Fk(j)p Fo(t)1420 3067 y Fj(1)p Fn(\000)p Fm(\033)1557 3108 y Fp(\000)p Fk(j)1646 3028 y Fi(\001)1691 3108 y Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)27 b(!)h Fp(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(:)547 b Fp(\(7.3\))386 3258 y(Here)35 b(the)h(input)f(of)f Fo(\016)39 b Fp(in)c(Prop)s(osition)g(5.1)f(sa)m (y)i Fo(\016)2262 3273 y Fj(1)2337 3258 y Fp(\(needed)g(to)e(\014x)i (the)f Fo(m)3219 3273 y Fj(0)3293 3258 y Fp(in)386 3375 y(the)k(de\014nition)h(of)e(the)i(\000)e(of)h(Corollary)g(5.2\))f(is)i (di\013eren)m(t;)j(w)m(e)d(need)g(to)e(ha)m(v)m(e)386 3491 y Fo(\033)g(>)33 b(\027)642 3455 y Fn(0)666 3491 y Fp(,)k Fo(\027)784 3455 y Fn(0)841 3491 y Fp(=)c Fo(\027)998 3506 y Fj(1)1063 3491 y Fk(\000)25 b Fo(\016)1208 3506 y Fj(1)1247 3491 y Fp(,)37 b(for)f(whic)m(h)h Fo(\016)1789 3506 y Fj(1)1862 3491 y Fo(<)d(\016)40 b Fp(is)c(needed.)56 b(The)37 b(construction)g(of)386 3607 y(this)c(\000)g(dep)s(ends)h(on)e (the)h(same)h Fo(\017)f Fp(as)f(ab)s(o)m(v)m(e,)i(cf.)43 b(Section)34 b(6.)486 3723 y(Com)m(bining)f(\(7.2\))f(and)h(\(7.3\))f (leads)i(to)813 3893 y Fk(jj)p Fo( )t Fp(\()o Fo(t)p Fp(\))22 b Fk(\000)h Fo(F)1231 3908 y Fn(\000)1290 3813 y Fi(\000)1336 3893 y Fk(j)1389 3868 y Fp(\026)1364 3893 y Fo(A)p Fk(j)1465 3813 y Fi(\001)1510 3893 y Fo(F)1573 3908 y Fn(\000)1632 3813 y Fi(\000)1678 3893 y Fk(j)p Fo(t)1741 3852 y Fj(1)p Fn(\000)p Fm(\033)1878 3893 y Fp(\000)p Fk(j)1967 3813 y Fi(\001)2012 3893 y Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)k(!)h Fp(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(:)226 b Fp(\(7.4\))486 4064 y(By)33 b(com)m(bining)i (Corollary)e(6.2)g(and)h(\(7.4\))f(w)m(e)h(conclude)h(\(b)m(y)f (\014nally)g(\014xing)386 4180 y Fo(\017)28 b(>)g Fp(0)k(su\016cien)m (tly)j(small\))e(that)1397 4348 y Fk(jj)p Fo( )t Fp(\()o Fo(t)p Fp(\))p Fk(jj)27 b Fp(=)h(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(;)810 b Fp(\(7.5\))386 4517 y(and)33 b(therefore)g(that)f Fo( )g Fp(=)27 b(0)33 b(pro)m(ving)g(Theorem)h(1.1.)386 4698 y Fg(R)-5 b(emark)59 b Fp(7.2)p Fg(.)48 b Fp(With)g(the)g (assumption)h(\(2.9\))e(w)m(e)i(pro)s(ceed)f(similarly)h(using)386 4814 y(Remarks)34 b(5.3)e(and)g(6.3,)h(and)f(Lemma)i(7.1.)1252 5045 y(8.)49 b Fq(Pr)n(oof)38 b(of)h(Theorem)e(1.2)486 5219 y Fp(W)-8 b(e)36 b(shall)i(here)f(elab)s(orate)f(on)h(the)g(deriv) -5 b(ation)37 b(of)f(Theorem)h(1.2)g(from)f(our)386 5335 y(general)d(result)g(Theorem)h(1.1.)486 5451 y(First)e(w)m(e)i(remo)m (v)m(e)g(the)f(singularit)m(y)h(at)e Fo(x)c Fp(=)g(0)k(b)m(y)i (de\014ning)881 5623 y Fo(h)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f(2)1340 5582 y Fn(\000)p Fj(1)1434 5623 y Fo(\030)1482 5582 y Fj(2)1543 5623 y Fp(+)1656 5598 y(~)1641 5623 y Fo(V)22 b Fp(\()p Fo(x)p Fp(\);)2007 5598 y(~)1992 5623 y Fo(V)g Fp(\()p Fo(x)p Fp(\))28 b(=)f Fo(F)2396 5638 y Fj(+)2456 5623 y Fp(\()p Fk(j)p Fo(x)p Fk(j)p Fp(\))o Fo(V)22 b Fp(\()6 b(^)-55 b Fo(x)p Fp(\))p Fo(;)p eop end %%Page: 33 33 TeXDict begin 33 32 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(33)386 459 y Fp(where)30 b(\(as)f(b)s(efore\))g Fo(V)51 b Fp(is)29 b(a)g(Morse)h(function)g(on)e Fo(S)2288 423 y Fm(n)p Fn(\000)p Fj(1)2425 459 y Fp(.)43 b(\(See)30 b(Remarks)g(8.3)e(for)386 575 y(extensions.\))45 b(In)29 b(this)h(case)g(clearly)h(the)f(h)m(yp)s(otheses)h(\(H1\){\(H3\))e(of)g (Section)h(2)386 691 y(are)k(satis\014ed,)h(and)f(\(H4\))g(holds)g(for) g(an)m(y)g(critical)h(p)s(oin)m(t)e Fo(!)2611 706 y Fm(l)2667 691 y Fk(2)d Fo(C)2833 706 y Fm(r)2905 691 y Fp(and)k(energy)386 807 y Fo(E)57 b(>)50 b(V)22 b Fp(\()p Fo(!)819 822 y Fm(j)855 807 y Fp(\))46 b(up)s(on)g(putting)g Fo(!)t Fp(\()o Fo(E)6 b Fp(\))51 b(=)g Fo(!)2016 822 y Fm(l)2041 807 y Fp(,)f Fo(\030)5 b Fp(\()o Fo(E)h Fp(\))51 b(=)f Fo(k)s Fp(\()p Fo(E)6 b Fp(\))p Fo(!)2765 822 y Fm(l)2837 807 y Fp(and)46 b Fo(k)s Fp(\()p Fo(E)6 b Fp(\))51 b(=)386 852 y Fi(p)p 486 852 566 4 v 85 x Fp(2\()o Fo(E)28 b Fk(\000)23 b Fo(V)f Fp(\()p Fo(!)950 952 y Fm(l)975 937 y Fp(\)\).)486 1053 y(F)-8 b(or)31 b(\(1.6\))h(w)m(e)i(put)695 1239 y Fo(g)t Fp(\()o Fo(u;)17 b(\021)t(;)g(E)6 b Fp(\))26 b(=)1225 1149 y Fi(p)p 1325 1149 V 90 x Fp(2\()o Fo(E)i Fk(\000)23 b Fo(V)f Fp(\()p Fo(!)1789 1254 y Fm(l)1814 1239 y Fp(\)\))g Fk(\000)2012 1149 y Fi(p)p 2112 1149 928 4 v 90 x Fp(2)p Fo(E)28 b Fk(\000)22 b Fo(\021)2412 1210 y Fj(2)2473 1239 y Fk(\000)h Fp(2)p Fo(V)e Fp(\()p Fo(!)2799 1254 y Fm(l)2847 1239 y Fp(+)h Fo(u)p Fp(\))p Fo(;)386 1410 y Fp(yielding)35 b(\(1.7\))d(with)1170 1643 y Fo(A)p Fp(\()p Fo(E)6 b Fp(\))28 b(=)g Fo(k)s Fp(\()p Fo(E)6 b Fp(\))1737 1595 y Fn(\000)p Fj(1)1848 1503 y Fi(\022)2004 1586 y Fo(V)2082 1549 y Fj(\()q(2\))2177 1586 y Fp(\()p Fo(!)2276 1601 y Fm(l)2301 1586 y Fp(\))84 b(0)2147 1702 y(0)226 b Fo(I)2473 1503 y Fi(\023)2563 1643 y Fo(:)486 1895 y Fp(W)-8 b(e)50 b(ma)m(y)h(c)m(ho)s(ose)g(an)f (orthonormal)f(basis)i(in)f Fk(f)p Fo(!)2454 1910 y Fm(l)2480 1895 y Fk(g)2530 1847 y Fn(?)2646 1895 y Fk(\022)58 b FC(R)2865 1859 y Fm(n)2962 1895 y Fp(for)49 b(whic)m(h)386 2015 y Fo(V)464 1978 y Fj(\()q(2\))559 2015 y Fp(\()p Fo(!)658 2030 y Fm(l)683 2015 y Fp(\))28 b(is)f(diagonal,)i(sa)m(y)f Fo(V)1496 1978 y Fj(\()q(2\))1591 2015 y Fp(\()p Fo(!)1690 2030 y Fm(l)1715 2015 y Fp(\))g(=)f(diag)18 b(\()p Fo(q)2162 2030 y Fj(1)2202 2015 y Fo(;)f(:)g(:)g(:)f(;)h(q)2464 2030 y Fm(n)p Fn(\000)p Fj(1)2601 2015 y Fp(\).)41 b(The)29 b(eigen)m(v)-5 b(alues)386 2131 y(of)32 b Fo(B)5 b Fp(\()p Fo(E)h Fp(\))33 b(tak)m(e)g(the)g(form)952 2351 y Fo(\014)1013 2309 y Fj(+)1007 2376 y Fm(j)1072 2351 y Fp(\()p Fo(E)6 b Fp(\))28 b(=)f Fk(\000)1444 2283 y Fp(1)p 1444 2328 49 4 v 1444 2419 a(2)1525 2351 y(+)1633 2283 y(1)p 1633 2328 V 1633 2419 a(2)1692 2232 y Fi(q)p 1792 2232 865 4 v 119 x Fp(1)22 b Fk(\000)g Fp(2)p Fo(q)2054 2366 y Fm(j)2091 2351 y Fo(=)p Fp(\()p Fo(E)28 b Fk(\000)22 b Fo(V)g Fp(\()p Fo(!)2555 2366 y Fm(l)2581 2351 y Fp(\)\))32 b(or)952 2588 y Fo(\014)1013 2547 y Fn(\000)1007 2613 y Fm(j)1072 2588 y Fp(\()p Fo(E)6 b Fp(\))28 b(=)f Fk(\000)1444 2521 y Fp(1)p 1444 2565 49 4 v 1444 2656 a(2)1525 2588 y Fk(\000)1635 2521 y Fp(1)p 1635 2565 V 1635 2656 a(2)1694 2469 y Fi(q)p 1793 2469 865 4 v 1793 2588 a Fp(1)22 b Fk(\000)h Fp(2)p Fo(q)2056 2603 y Fm(j)2093 2588 y Fo(=)p Fp(\()o Fo(E)28 b Fk(\000)23 b Fo(V)f Fp(\()p Fo(!)2557 2603 y Fm(l)2582 2588 y Fp(\)\))3174 2462 y(\(8.1\))386 2803 y(sa)m(y)33 b(with)777 2728 y Fk(p)p 860 2728 51 4 v 75 x Fo(\020)h Fp(:=)28 b Fo(i)1101 2728 y Fk(p)p 1184 2728 128 4 v 75 x(\000)p Fo(\020)41 b Fp(if)32 b Fo(\020)j(<)27 b Fp(0.)486 2919 y(Clearly)33 b(the)g(h)m(yp)s(othesis)i (\(H5\))d(is)h(the)g(non-degeneracy)h(condition,)f Fo(q)3158 2934 y Fm(j)3222 2919 y Fk(6)p Fp(=)28 b(0)386 3035 y(for)i(all)h Fo(j)6 b Fp(,)31 b(while)h(h)m(yp)s(othesis)h(\(H6\))d(amoun)m(ts)i(to) e Fo(q)2283 3050 y Fm(j)2347 3035 y Fo(<)e Fp(0)i(for)h(some)g Fo(j)6 b Fp(,)31 b(i.e.)44 b Fo(!)3253 3050 y Fm(l)3309 3035 y Fp(is)386 3151 y(a)32 b(lo)s(cal)h(maxim)m(um)h(or)e(a)g(saddle) i(p)s(oin)m(t)f(of)f Fo(V)21 b Fp(.)486 3268 y(As)45 b(for)e(\(H7\))i(one)f(easily)i(c)m(hec)m(ks)h(that)e(there)g(exists)h (a)e(smo)s(oth)h(basis)g(of)386 3390 y(eigen)m(v)m(ectors)35 b(of)d Fo(B)5 b Fp(\()p Fo(E)h Fp(\))1275 3342 y Fm(tr)1371 3390 y Fp(for)32 b Fo(E)c Fk(\000)23 b Fo(V)f Fp(\()p Fo(!)1898 3405 y Fm(l)1923 3390 y Fp(\))28 b Fk(2)g Fp(\(0)p Fo(;)17 b Fk(1)p Fp(\))k Fk(n)h(f)p Fp(2)p Fo(q)2587 3405 y Fj(1)2626 3390 y Fo(;)17 b(:)g(:)g(:)f(;)h Fp(2)p Fo(q)2937 3405 y Fm(n)p Fn(\000)p Fj(1)3074 3390 y Fk(g)p Fp(.)486 3506 y(Elemen)m(tary)23 b(analyticit)m(y)h(argumen)m(ts)e(sho) m(w)h(that)f(giv)m(en)h(an)m(y)f Fo(m)28 b Fk(2)g(f)p Fp(2)p Fo(;)17 b Fp(3)p Fo(;)g(:)g(:)g(:)e Fk(g)386 3623 y Fp(the)35 b(set)h(of)e(resonances)j(of)d(order)h Fo(m)g Fp(for)f(an)m(y)i(of)e(the)h(eigen)m(v)-5 b(alues)37 b(of)d Fo(B)5 b Fp(\()p Fo(E)h Fp(\))35 b(is)386 3739 y(discrete)f(in)f(\()p Fo(V)21 b Fp(\()p Fo(!)1073 3754 y Fm(l)1099 3739 y Fp(\))p Fo(;)c Fk(1)p Fp(\))o(.)486 3855 y(In)48 b(conclusion,)54 b(the)49 b(h)m(yp)s(otheses)i (\(H1\){\(H8\))d(are)g(satis\014ed)i(for)e(an)m(y)h(lo-)386 3971 y(cal)j(maxim)m(um)h(or)e(saddle)h(p)s(oin)m(t)g Fo(!)1821 3986 y Fm(l)1898 3971 y Fp(of)f(a)g(Morse)i(function)f Fo(V)73 b Fp(for)51 b Fo(E)3209 3986 y Fj(0)3308 3971 y Fk(2)386 4088 y Fp(\()p Fo(V)21 b Fp(\()p Fo(!)601 4103 y Fm(l)627 4088 y Fp(\))p Fo(;)c Fk(1)p Fp(\))k Fk(n)h(D)36 b Fp(where)d Fk(D)i Fp(is)f(discrete)g(in)f(\()p Fo(V)21 b Fp(\()p Fo(!)2232 4103 y Fm(l)2258 4088 y Fp(\))p Fo(;)c Fk(1)p Fp(\))o(.)486 4204 y(Due)22 b(to)g(the)i(p)s(ossible)g (existence)h(of)d(b)s(ound)h(states)g(w)m(e)h(c)m(hange)g(the)f (de\014nition)386 4320 y(of)32 b Fo(P)560 4335 y Fm(l)618 4320 y Fp(to)h(b)s(e)1128 4450 y Fo(P)1191 4465 y Fm(l)1245 4450 y Fp(=)27 b Fo(s)22 b Fk(\000)39 b Fp(lim)1516 4510 y Fm(t)p Fn(!1)1699 4450 y Fo(e)1744 4409 y Fm(itH)1861 4450 y Fo(\037)1922 4465 y Fm(l)1948 4450 y Fp(\()6 b(^)-55 b Fo(x)q Fp(\))p Fo(e)2125 4409 y Fn(\000)p Fm(itH)2296 4450 y Fo(E)2368 4465 y Fm(ac)2441 4450 y Fp(\()p Fo(H)8 b Fp(\))o Fo(;)386 4638 y Fp(where)28 b Fo(E)734 4653 y Fm(ac)807 4638 y Fp(\()p Fo(H)8 b Fp(\))26 b(is)i(the)f(orthogonal)f (pro)5 b(jection)28 b(on)m(to)f(the)g(absolutely)i(con)m(tin)m(u-)386 4754 y(ous)h(subspace)j(of)c Fo(H)8 b Fp(,)31 b(see)g([H])f(and)h([A)m (CH,)g(Theorem)g(C.1].)43 b(This)32 b(giv)m(es)f(\(1.12\))386 4870 y(with)i(the)g(left)g(hand)g(side)g(replaced)h(b)m(y)g Fo(E)1979 4885 y Fm(ac)2051 4870 y Fp(\()p Fo(H)8 b Fp(\))o(.)486 4987 y(No)m(w,)31 b(to)f(get)g(\(1.14\))f(it)h(su\016ces)i(b)m(y)f (Theorem)h(1.1)d(to)h(v)m(erify)j(\(1.13\))c(for)h(an)m(y)386 5103 y Fo(E)458 5118 y Fj(0)525 5103 y Fk(2)e Fp(\()p Fo(V)22 b Fp(\()p Fo(!)835 5118 y Fm(l)860 5103 y Fp(\))p Fo(;)17 b Fk(1)p Fp(\).)43 b(In)m(v)m(oking)34 b(the)f(discreteness)j (of)c(the)h(set)h(of)e(eigen)m(v)-5 b(alues)34 b(of)386 5219 y Fo(H)g Fp(on)26 b(the)h(complemen)m(t)h(of)e(the)h(set)g(of)f (critical)h(v)-5 b(alues)27 b(of)f Fo(V)c Fp(,)27 b(cf.)42 b([A)m(CH,)27 b(Theo-)386 5335 y(rem)i(C.1],)h(one)f(ma)m(y)g(easily)h (conclude)g(\(1.13\))e(from)g(the)h(follo)m(wing)g(statemen)m(t:)486 5451 y(Consider)34 b(an)m(y)f(op)s(en)g(set)g Fo(I)1508 5466 y Fj(0)1575 5451 y Fk(\022)28 b Fp(\()p Fo(V)22 b Fp(\()p Fo(!)1896 5466 y Fm(l)1921 5451 y Fp(\))p Fo(;)17 b Fk(1)p Fp(\))32 b(suc)m(h)i(that)1308 5623 y Fo(I)1351 5638 y Fj(0)1412 5623 y Fk(\\)23 b Fp(\()p Fo(\033)1594 5638 y Fm(pp)1670 5623 y Fp(\()o Fo(H)8 b Fp(\))22 b Fk([)h Fo(V)e Fp(\()p Fo(C)2131 5638 y Fm(r)2169 5623 y Fp(\)\))27 b(=)h Fk(;)p Fo(:)p eop end %%Page: 34 34 TeXDict begin 34 33 bop 386 259 a Fl(34)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)386 459 y Fp(Let)e Fk(H)635 474 y Fj(0)697 459 y Fp(b)s(e)f(the)h(closure)h(of)e(the)h(subspace)h (of)e(states)h Fo( )32 b Fp(=)c Fo(f)11 b Fp(\()o Fo(H)d Fp(\))p Fo( )t Fp(,)24 b Fo(f)39 b Fk(2)28 b Fo(C)3115 423 y Fn(1)3108 483 y Fj(0)3189 459 y Fp(\()p Fo(I)3270 474 y Fj(0)3310 459 y Fp(\),)386 575 y(ob)s(eying)34 b(\(1.8\))e(and)h(\(1.9\).)43 b(Then)34 b(for)e(all)g Fo( )g Fp(=)c Fo(P)2245 590 y Fm(l)2270 575 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo( )36 b Fp(where)e Fo(f)k Fk(2)28 b Fo(C)3132 539 y Fn(1)3125 600 y Fj(0)3207 575 y Fp(\()p Fo(I)3288 590 y Fj(0)3327 575 y Fp(\))1711 738 y Fo( )j Fk(2)d(H)1983 753 y Fj(0)2023 738 y Fo(:)1124 b Fp(\(8.2\))486 900 y(W)-8 b(e)42 b(shall)g(v)m(erify)h(\(8.2\))e(b)m (y)i(sho)m(wing)f(that)g(indeed)h Fo( )k Fp(=)c Fo(P)2778 915 y Fm(l)2804 900 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )46 b Fp(ob)s(eys)386 1016 y(\(1.8\))35 b(and)i(\(1.9\))o(.)54 b(W)-8 b(e)37 b(shall)f(pro)s(ceed)h(a)f(little)g(more)h(generally)g (than)f(needed)386 1133 y(in)d(that)f(w)m(e)i(here)f(assume)h(that)f (the)g Fk(U)1845 1148 y Fj(0)1917 1133 y Fp(of)39 b(\(1.9\))32 b(is)h(giv)m(en)h(b)m(y)566 1304 y Fk(U)628 1319 y Fj(0)696 1304 y Fp(=)27 b Fk(U)861 1319 y Fm(\017)922 1304 y Fp(=)1044 1278 y(~)1026 1304 y Fk(C)1078 1319 y Fm(\017)1133 1304 y Fk(\002)22 b FC(R)1316 1262 y Fm(n)1363 1304 y Fp(;)585 1446 y(~)566 1471 y Fk(C)618 1486 y Fm(\017)679 1471 y Fp(=)28 b Fk(f)o Fo(x)h Fk(2)f FC(R)1094 1430 y Fm(n)1162 1471 y Fk(n)22 b(f)p Fp(0)p Fk(gj)6 b Fp(^)-55 b Fo(x)28 b Fk(2)g(C)1640 1486 y Fm(\017)1673 1471 y Fk(g)p Fo(;)114 b Fk(C)1916 1486 y Fm(\017)1977 1471 y Fp(=)2080 1391 y Fi(\010)2138 1471 y Fo(!)31 b Fk(2)d Fo(S)2390 1430 y Fm(n)p Fn(\000)p Fj(1)2555 1471 y Fk(j)f(j)p Fo(!)e Fk(\000)e Fo(!)2885 1486 y Fm(l)2911 1471 y Fk(j)k Fo(<)h(\017)3109 1391 y Fi(\011)3167 1471 y Fo(;)386 1640 y Fp(where)34 b Fo(\017)28 b(>)f Fp(0)33 b(is)g(tak)m(en)g(so)g(small)g(that)g Fk(C)1922 1655 y Fm(\017)1977 1640 y Fk(\\)22 b Fo(C)2135 1655 y Fm(r)2201 1640 y Fp(=)27 b Fk(f)p Fo(!)2415 1655 y Fm(l)2441 1640 y Fk(g)p Fp(.)486 1765 y(Pic)m(k)726 1739 y(~)705 1765 y Fo(f)40 b Fk(2)30 b Fo(C)966 1729 y Fn(1)959 1790 y Fj(0)1041 1765 y Fp(\()p Fo(I)1122 1780 y Fj(0)1161 1765 y Fp(\))k(suc)m(h)h(that)f(0)29 b Fk(\024)1873 1739 y Fp(~)1852 1765 y Fo(f)41 b Fk(\024)30 b Fp(1)j(and)2342 1739 y(~)2321 1765 y Fo(f)40 b Fp(=)30 b(1)j(in)h(a)g(neigh)m(b)s(orho)s(o)s(d)386 1882 y(of)e(supp)18 b(\()p Fo(f)11 b Fp(\))o(.)44 b(Let)32 b Fo(r)f Fk(2)d Fo(C)1340 1845 y Fn(1)1415 1882 y Fp(\()p FC(R)1537 1845 y Fm(n)1583 1882 y Fp(\))33 b(b)s(e)f(giv)m(en)i(in)f(terms)g(of)f(an)m (y)i Fo(F)2785 1897 y Fj(+)2872 1882 y Fk(2)28 b(F)3038 1897 y Fj(+)3129 1882 y Fp(b)m(y)1134 2120 y Fo(r)s Fp(\()p Fo(x)p Fp(\))g(=)1443 1985 y Fi(Z)1543 2011 y Fn(j)p Fm(x)p Fn(j)1499 2210 y Fj(0)1642 2120 y Fo(F)1705 2135 y Fj(+)1765 2120 y Fp(\()p Fo(s)p Fp(\))o Fo(ds)22 b Fp(+)2103 1985 y Fi(Z)2203 2011 y Fj(1)2159 2210 y(0)2259 2120 y Fo(F)2322 2135 y Fn(\000)2381 2120 y Fp(\()p Fo(s)p Fp(\))p Fo(ds:)547 b Fp(\(8.3\))386 2340 y(\(Notice)33 b(that)f Fo(r)s Fp(\()p Fo(x)p Fp(\))c(=)g Fk(j)p Fo(x)p Fk(j)k Fp(for)g Fk(j)p Fo(x)p Fk(j)27 b(\025)i Fp(1.\))43 b(Let)970 2551 y Fo(p)1019 2566 y Fn(jj)1089 2551 y Fp(=)1203 2483 y(1)p 1203 2528 49 4 v 1203 2619 a(2)1262 2551 y(\()p Fk(r)p Fo(r)25 b Fk(\001)c Fo(p)h Fp(+)g Fo(h:c:)p Fp(\))q Fo(;)122 b Fp(~)-57 b Fo(p)2051 2566 y Fn(jj)2122 2551 y Fp(=)2247 2525 y(~)2225 2551 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(p)2498 2566 y Fn(jj)2562 2525 y Fp(~)2541 2551 y Fo(f)j Fp(\()p Fo(H)d Fp(\))o Fo(:)386 2764 y FC(Lemma)39 b(8.1.)j Fg(L)-5 b(et)36 b Fo(\037)1229 2779 y Fm(l)1283 2764 y Fk(2)28 b Fo(C)1454 2727 y Fn(1)1447 2788 y Fj(0)1529 2764 y Fp(\()p Fk(C)1619 2779 y Fm(\017)1652 2764 y Fp(\))35 b Fg(b)-5 b(e)35 b(given)f(with)h Fp(0)28 b Fk(\024)g Fo(\037)2554 2779 y Fm(l)2608 2764 y Fk(\024)h Fp(1)35 b Fg(and)f Fo(\037)3048 2779 y Fm(l)3102 2764 y Fp(=)28 b(1)35 b Fg(in)386 2880 y(a)g(neighb)-5 b(orho)g(o)g(d)33 b(of)h Fo(!)1225 2895 y Fm(l)1251 2880 y Fg(,)h(and)j Fp(~)-53 b Fo(g)1552 2895 y Fj(2)1619 2880 y Fk(2)28 b Fo(C)1790 2844 y Fn(1)1783 2904 y Fj(0)1865 2880 y Fp(\()p FC(R)p Fp(\))34 b Fg(by)1153 3052 y Fp(~)-52 b Fo(g)1197 3067 y Fj(2)1236 3052 y Fp(\()p Fo(s)p Fp(\))27 b(=)1510 3026 y(~)1489 3052 y Fo(f)1548 2971 y Fi(\000)1593 3052 y Fp(2)1642 3011 y Fn(\000)p Fj(1)1736 3052 y Fo(s)1782 3011 y Fj(2)1844 3052 y Fp(+)22 b Fo(V)f Fp(\()p Fo(!)2119 3067 y Fm(l)2145 3052 y Fp(\))2183 2971 y Fi(\001)2229 3052 y Fp(1)2278 3067 y Fj(\(0)p Fm(;)p Fn(1)p Fj(\))2462 3052 y Fp(\()p Fo(s)p Fp(\))p Fo(:)386 3223 y Fg(L)-5 b(et)35 b(r)-5 b(e)g(al-value)g(d)34 b Fo(g)1087 3182 y Fn(\000)1083 3247 y Fj(1)1145 3223 y Fo(;)17 b(g)1240 3182 y Fj(+)1236 3247 y(1)1326 3223 y Fk(2)28 b Fo(C)1497 3187 y Fn(1)1490 3247 y Fj(0)1572 3223 y Fp(\()p FC(R)p Fp(\))34 b Fg(b)-5 b(e)35 b(given)f(with)693 3387 y Fo(c)735 3346 y Fn(\000)735 3412 y Fj(+)822 3387 y Fo(<)29 b Fp(~)-51 b Fo(c)967 3402 y Fn(\000)1026 3387 y Fp(;)116 b Fo(c)1211 3346 y Fn(\000)1211 3412 y Fj(+)1298 3387 y Fp(=)28 b(sup)1565 3306 y Fi(\000)1611 3387 y Fp(supp)1829 3306 y Fi(\000)1874 3387 y Fo(g)1925 3346 y Fn(\000)1921 3412 y Fj(1)1984 3306 y Fi(\001)o(\001)2075 3387 y Fo(;)118 b Fp(~)-51 b Fo(c)2260 3402 y Fn(\000)2347 3387 y Fp(=)27 b(inf)d(\(supp)18 b(\()s(~)-52 b Fo(g)2926 3402 y Fj(2)2965 3387 y Fp(\)\))p Fo(;)693 3548 y(c)735 3507 y Fj(+)735 3573 y Fn(\000)822 3548 y Fo(>)29 b Fp(~)-51 b Fo(c)967 3563 y Fj(+)1026 3548 y Fp(;)116 b Fo(c)1211 3507 y Fj(+)1211 3573 y Fn(\000)1298 3548 y Fp(=)28 b(inf)1536 3467 y Fi(\000)1582 3548 y Fp(supp)1800 3467 y Fi(\000)1845 3548 y Fo(g)1896 3507 y Fj(+)1892 3573 y(1)1955 3467 y Fi(\001)o(\001)2046 3548 y Fo(;)118 b Fp(~)-51 b Fo(c)2231 3563 y Fj(+)2318 3548 y Fp(=)28 b(sup)17 b(\(supp)h(\()s(~)-52 b Fo(g)2926 3563 y Fj(2)2965 3548 y Fp(\)\))p Fo(:)386 3711 y Fg(L)-5 b(et)35 b Fo(F)617 3726 y Fj(+)704 3711 y Fk(2)28 b(F)870 3726 y Fj(+)929 3711 y Fg(,)34 b Fo(F)1056 3726 y Fn(\000)1143 3711 y Fk(2)28 b(F)1309 3726 y Fn(\000)1403 3711 y Fg(and)1103 3886 y Fo(C)34 b(>)28 b Fp(2)1360 3796 y Fi(p)p 1459 3796 1172 4 v 1459 3886 a Fp(2\(sup)17 b(\(supp)h(\()p Fo(f)11 b Fp(\)\))22 b Fk(\000)g Fp(min)c(\()o Fo(V)k Fp(\)\))p Fo(:)386 4048 y Fg(Then,)34 b(in)g(the)h(state)g Fo( )t Fp(\()p Fo(t)p Fp(\))28 b(=)g Fo(e)1540 4012 y Fn(\000)p Fm(itH)1712 4048 y Fo(P)1775 4063 y Fm(l)1800 4048 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo( )558 4128 y Fi(Z)674 4183 y(\012)721 4263 y Fo(r)768 4222 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\016)951 4183 y Fi(\013)998 4302 y Fm(t)1027 4263 y Fo(dt)28 b(<)f Fk(1)p Fp(;)116 b Fo(\016)32 b(>)c Fp(0)p Fo(;)1432 b Fp(\(8.4\))558 4387 y Fi(Z)674 4522 y Fk(j)702 4441 y Fi(\012)749 4522 y Fo(p)22 b Fk(\001)g Fo(r)917 4481 y Fj(\(2\))1011 4522 y Fo(p)1060 4441 y Fi(\013)1107 4561 y Fm(t)1136 4522 y Fk(j)p Fo(dt)28 b(<)f Fk(1)p Fo(;)1666 b Fp(\(8.5\))558 4645 y Fi(Z)674 4670 y(D)735 4781 y Fo(r)s Fk(jr)908 4756 y Fp(~)893 4781 y Fo(V)21 b Fk(j)999 4740 y Fj(2)1038 4670 y Fi(E)1099 4850 y Fm(t)1128 4781 y Fo(dt)28 b(<)g Fk(1)p Fo(;)1701 b Fp(\(8.6\))558 4904 y Fi(Z)674 4929 y(D)747 5040 y Fp(~)-61 b Fo(\037)796 5055 y Fm(l)822 5040 y Fo(r)869 4999 y Fn(\000)934 4971 y Fh(1)p 934 4983 31 3 v 934 5025 a(2)978 4959 y Fi(\000)1024 5040 y Fo(\021)1076 4999 y Fj(2)1137 5040 y Fp(+)22 b Fo(u)1291 4999 y Fj(2)1330 4959 y Fi(\001)1376 5040 y Fo(r)1423 4999 y Fn(\000)1488 4971 y Fh(1)p 1487 4983 V 1487 5025 a(2)1543 5040 y Fp(~)-60 b Fo(\037)1593 5055 y Fm(l)1619 4929 y Fi(E)1680 5109 y Fm(t)1709 5040 y Fo(dt)28 b(<)g Fk(1)p Fp(;)127 b(~)-61 b Fo(\037)2230 5055 y Fm(l)2284 5040 y Fp(=)28 b Fo(\037)2449 5055 y Fm(l)2475 5040 y Fp(\()6 b(^)-55 b Fo(x)p Fp(\))p Fo(F)2669 5055 y Fj(+)2728 5040 y Fp(\()p Fo(r)s Fp(\))p Fo(;)296 b Fp(\(8.7\))558 5165 y Fi(Z)657 5191 y Fn(1)613 5391 y Fj(1)749 5301 y Fk(\000)p Fo(t)861 5260 y Fn(\000)p Fj(1)956 5220 y Fi(\012)1003 5301 y Fo(F)1080 5260 y Fn(0)1066 5325 y(\000)1125 5220 y Fi(\000)1171 5301 y Fo(C)1248 5260 y Fn(\000)p Fj(1)1342 5301 y Fo(t)1377 5260 y Fn(\000)p Fj(1)1472 5301 y Fo(r)1519 5220 y Fi(\001)o(\013)1611 5340 y Fm(t)1641 5301 y Fo(dt)27 b(<)h Fk(1)p Fo(;)1189 b Fp(\(8.8\))558 5430 y Fi(Z)657 5457 y Fn(1)613 5656 y Fj(1)749 5566 y Fo(t)784 5525 y Fn(\000)p Fj(1)878 5566 y Fk(jj)p Fo(g)985 5485 y Fi(\000)1038 5566 y Fp(~)-57 b Fo(p)1079 5581 y Fn(jj)1122 5485 y Fi(\001)1168 5566 y Fo(F)1231 5581 y Fn(\000)1290 5485 y Fi(\000)1335 5566 y Fo(C)1412 5525 y Fn(\000)p Fj(1)1507 5566 y Fo(t)1542 5525 y Fn(\000)p Fj(1)1636 5566 y Fo(r)1683 5485 y Fi(\001)1729 5566 y Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)1963 5525 y Fj(2)2001 5566 y Fo(dt)28 b(<)g Fk(1)p Fp(;)828 b(\(8.9\))p eop end %%Page: 35 35 TeXDict begin 35 34 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(35)641 459 y Fo(g)31 b Fk(2)d Fo(C)890 418 y Fn(1)883 483 y Fj(0)965 459 y Fp(\()o(\()p Fk(\0001)p Fo(;)17 b Fp(0\)\))p Fo(;)120 b Fp(\026)-53 b Fo(g)31 b Fp(=)d Fo(g)t(;)558 537 y Fi(Z)657 564 y Fn(1)613 763 y Fj(1)749 673 y Fo(t)784 632 y Fn(\000)p Fj(1)878 673 y Fk(jj)934 592 y Fi(\000)979 673 y Fp(1)22 b Fk(\000)k Fp(~)-52 b Fo(g)1197 688 y Fj(2)1236 592 y Fi(\000)1290 673 y Fp(~)-57 b Fo(p)1331 689 y Fn(jj)1374 592 y Fi(\001\001)1465 673 y Fo(F)1528 688 y Fn(\000)1587 592 y Fi(\000)1633 673 y Fo(C)1710 632 y Fn(\000)p Fj(1)1804 673 y Fo(t)1839 632 y Fn(\000)p Fj(1)1934 673 y Fo(r)1981 592 y Fi(\001)2038 673 y Fp(~)c Fo(\037)2087 688 y Fm(l)2113 673 y Fo( )t Fp(\()p Fo(t)p Fp(\))q Fk(jj)2348 632 y Fj(2)2386 673 y Fo(dt)28 b(<)f Fk(1)p Fo(;)395 b Fp(\(8.10\))558 803 y Fi(Z)657 829 y Fn(1)613 1028 y Fj(1)749 938 y Fo(t)784 897 y Fn(\000)p Fj(1)878 938 y Fk(jj)p Fo(B)1013 897 y Fn(\000)1072 938 y Fp(\()p Fo(t)p Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)1417 897 y Fj(2)1456 938 y Fo(dt)27 b(<)h Fk(1)p Fp(;)116 b Fo(B)1995 897 y Fn(\000)2054 938 y Fp(\()p Fo(t)p Fp(\))28 b(=)f Fo(g)2347 897 y Fn(\000)2343 963 y Fj(1)2406 858 y Fi(\000)2451 938 y Fo(t)2486 897 y Fn(\000)p Fj(1)2581 938 y Fo(r)2628 858 y Fi(\001)2677 938 y Fp(~)-53 b Fo(g)2720 953 y Fj(2)2759 858 y Fi(\000)2813 938 y Fp(~)c Fo(p)2854 954 y Fn(jj)2897 858 y Fi(\001)2943 938 y Fo(;)155 b Fp(\(8.11\))558 1068 y Fi(Z)657 1094 y Fn(1)613 1293 y Fj(1)749 1203 y Fo(t)784 1162 y Fn(\000)p Fj(1)878 1203 y Fk(jj)p Fo(B)1013 1162 y Fj(+)1072 1203 y Fp(\()p Fo(t)p Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)1417 1162 y Fj(2)1456 1203 y Fo(dt)27 b(<)h Fk(1)p Fp(;)116 b Fo(B)1995 1162 y Fj(+)2054 1203 y Fp(\()p Fo(t)p Fp(\))28 b(=)f Fo(g)2347 1162 y Fj(+)2343 1228 y(1)2406 1123 y Fi(\000)2451 1203 y Fo(t)2486 1162 y Fn(\000)p Fj(1)2581 1203 y Fo(r)2628 1123 y Fi(\001)2677 1203 y Fp(~)-53 b Fo(g)2720 1218 y Fj(2)2759 1123 y Fi(\000)2813 1203 y Fp(~)c Fo(p)2854 1219 y Fn(jj)2897 1123 y Fi(\001)2943 1203 y Fo(:)155 b Fp(\(8.12\))386 1435 y Fg(Pr)-5 b(o)g(of.)41 b Fp(F)-8 b(or)39 b(\(8.4\),)i(\(8.5\))f(and)g(\(8.6\))f(w)m(e)i(refer) g(to)e([H])h(and)g([A)m(CH,)h(Theorem)386 1551 y(C.1].)56 b(The)38 b(b)s(ound)f(\(8.7\))f(follo)m(ws)h(from)g(those)g(estimates)h (b)m(y)g(T)-8 b(a)m(ylor)37 b(expan-)386 1667 y(sion.)486 1783 y(As)c(for)f(\(8.8\))g(w)m(e)h(consider)h(the)f(\\propagation)f (observ)-5 b(able")1207 1942 y(\010\()p Fo(t)p Fp(\))28 b(=)g Fo(f)11 b Fp(\()o Fo(H)d Fp(\))p Fo(F)1806 1957 y Fn(\000)1865 1861 y Fi(\000)1910 1942 y Fo(C)1987 1901 y Fn(\000)p Fj(1)2082 1942 y Fo(t)2117 1901 y Fn(\000)p Fj(1)2211 1942 y Fo(r)2258 1861 y Fi(\001)2304 1942 y Fo(f)j Fp(\()o Fo(H)d Fp(\))p Fo(:)386 2099 y Fp(W)-8 b(e)33 b(ma)m(y)g(b)s(ound)g(its)g(Heisen)m(b)s(erg)h(deriv)-5 b(ativ)m(e)35 b(as)650 2257 y FC(D)p Fp(\010\()q Fo(t)p Fp(\))27 b Fk(\025)i(\000)p Fo(\017t)1202 2215 y Fn(\000)p Fj(1)1297 2257 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(F)1597 2215 y Fn(0)1583 2281 y(\000)1642 2176 y Fi(\000)1688 2257 y Fo(C)1765 2215 y Fn(\000)p Fj(1)1859 2257 y Fo(t)1894 2215 y Fn(\000)p Fj(1)1989 2257 y Fo(r)2036 2176 y Fi(\001)2081 2257 y Fo(f)j Fp(\()p Fo(H)d Fp(\))21 b(+)h Fo(O)2502 2176 y Fi(\000)2547 2257 y Fo(t)2582 2215 y Fn(\000)p Fj(2)2677 2176 y Fi(\001)2723 2257 y Fp(;)114 b Fo(\017)28 b(>)f Fp(0)p Fo(:)486 2415 y Fp(As)33 b(for)f(\(8.9\))g(w)m(e)h (consider)h(the)f(observ)-5 b(able)885 2582 y(\010\()p Fo(t)p Fp(\))28 b(=)1219 2556 y(~)1198 2582 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))p Fo(g)1472 2501 y Fi(\000)1525 2582 y Fp(~)-57 b Fo(p)1566 2597 y Fn(jj)1609 2501 y Fi(\001)1655 2582 y Fo(t)1690 2541 y Fn(\000)p Fj(1)1784 2582 y Fo(r)s(F)1894 2597 y Fn(\000)1953 2501 y Fi(\000)1999 2582 y Fo(C)2076 2541 y Fn(\000)p Fj(1)2170 2582 y Fo(t)2205 2541 y Fn(\000)p Fj(1)2299 2582 y Fo(r)2346 2501 y Fi(\001)2392 2582 y Fo(g)2443 2501 y Fi(\000)2496 2582 y Fp(~)g Fo(p)2537 2597 y Fn(jj)2580 2501 y Fi(\001)2647 2556 y Fp(~)2626 2582 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))p Fo(:)386 2739 y Fp(W)-8 b(e)33 b(write)g(its)g(Heisen)m(b)s(erg)i(deriv)-5 b(ativ)m(e)34 b(as)585 2896 y FC(D)p Fp(\010\()p Fo(t)p Fp(\))28 b(=)g Fo(T)1041 2911 y Fj(1)1103 2896 y Fp(+)22 b Fo(T)1258 2911 y Fj(2)1319 2896 y Fp(+)g Fo(T)1474 2911 y Fj(3)1514 2896 y Fp(;)585 3065 y Fo(T)642 3080 y Fj(1)709 3065 y Fp(=)834 3039 y(~)813 3065 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))1036 2984 y Fi(\000)1082 3065 y FC(D)p Fo(g)1219 2984 y Fi(\000)1272 3065 y Fp(~)-57 b Fo(p)1313 3081 y Fn(jj)1356 2984 y Fi(\001\001)1447 3065 y Fo(t)1482 3024 y Fn(\000)p Fj(1)1577 3065 y Fo(r)s(F)1687 3080 y Fn(\000)1746 2984 y Fi(\000)1791 3065 y Fo(C)1868 3024 y Fn(\000)p Fj(1)1963 3065 y Fo(t)1998 3024 y Fn(\000)p Fj(1)2092 3065 y Fo(r)2139 2984 y Fi(\001)2184 3065 y Fo(g)2235 2984 y Fi(\000)2289 3065 y Fp(~)f Fo(p)2329 3081 y Fn(jj)2373 2984 y Fi(\001)2440 3039 y Fp(~)2418 3065 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))22 b(+)g Fo(h:c:;)585 3234 y(T)642 3249 y Fj(2)709 3234 y Fp(=)28 b(2)862 3193 y Fn(\000)p Fj(1)977 3208 y Fp(~)956 3234 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(g)1230 3153 y Fi(\000)1283 3234 y Fp(~)-57 b Fo(p)1324 3249 y Fn(jj)1367 3153 y Fi(\001)1413 3234 y Fo(t)1448 3193 y Fn(\000)p Fj(1)1543 3234 y Fo(r)1590 3153 y Fi(\000)1635 3234 y FC(D)p Fo(F)1784 3249 y Fn(\000)1843 3153 y Fi(\000)1889 3234 y Fo(C)1966 3193 y Fn(\000)p Fj(1)2060 3234 y Fo(t)2095 3193 y Fn(\000)p Fj(1)2190 3234 y Fo(r)2237 3153 y Fi(\001)o(\001)2328 3234 y Fo(g)2379 3153 y Fi(\000)2432 3234 y Fp(~)g Fo(p)2473 3249 y Fn(jj)2516 3153 y Fi(\001)2583 3208 y Fp(~)2561 3234 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))22 b(+)g Fo(h:c:;)585 3403 y(T)642 3418 y Fj(3)709 3403 y Fp(=)28 b(2)862 3361 y Fn(\000)p Fj(1)977 3376 y Fp(~)956 3403 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(g)1230 3322 y Fi(\000)1283 3403 y Fp(~)-57 b Fo(p)1324 3418 y Fn(jj)1367 3322 y Fi(\001\000)1459 3403 y FC(D)1545 3322 y Fi(\000)1590 3403 y Fo(t)1625 3361 y Fn(\000)p Fj(1)1720 3403 y Fo(r)1767 3322 y Fi(\001)o(\001)1858 3403 y Fo(F)1921 3418 y Fn(\000)1980 3322 y Fi(\000)2026 3403 y Fo(C)2103 3361 y Fn(\000)p Fj(1)2197 3403 y Fo(t)2232 3361 y Fn(\000)p Fj(1)2327 3403 y Fo(r)2374 3322 y Fi(\001)2419 3403 y Fo(g)2470 3322 y Fi(\000)2523 3403 y Fp(~)g Fo(p)2564 3418 y Fn(jj)2607 3322 y Fi(\001)2674 3376 y Fp(~)2653 3403 y Fo(f)11 b Fp(\()o Fo(H)d Fp(\))22 b(+)g Fo(h:c:;)386 3560 y Fp(and)33 b(notice)g(the)g(iden)m(tities)1093 3717 y FC(D)p Fo(r)d Fp(=)e Fo(p)1406 3733 y Fn(jj)1449 3717 y Fo(;)114 b FC(D)p Fo(p)1725 3733 y Fn(jj)1796 3717 y Fp(=)28 b Fo(p)22 b Fk(\001)g Fo(r)2068 3676 y Fj(\(2\))2162 3717 y Fo(p)g Fp(+)g Fo(O)2409 3636 y Fi(\000)2454 3717 y Fo(r)2501 3676 y Fn(\000)p Fj(3)2595 3636 y Fi(\001)2640 3717 y Fo(:)458 b Fp(\(8.13\))486 3876 y(Using)28 b(\(8.4\),)h(\(8.5\),)g(the) f(second)i(iden)m(tit)m(y)g(of)d(\(8.13\))h(and)g(\(3.11\))g(w)m(e)h (readily)386 3992 y(obtain)j(after)h(symmetrization)h(that)1483 4063 y Fi(Z)1583 4089 y Fn(1)1539 4289 y Fj(1)1674 4199 y Fk(jh)p Fo(T)1798 4214 y Fj(1)1837 4199 y Fk(i)1876 4228 y Fm(t)1906 4199 y Fk(j)p Fo(dt)27 b(<)h Fk(1)p Fo(:)847 b Fp(\(8.14\))486 4413 y(As)30 b(for)f(the)g(the)h(term)g Fo(T)1389 4428 y Fj(2)1458 4413 y Fp(w)m(e)h(use)f(the)g(\014rst)g (iden)m(tit)m(y)i(of)d(\(8.13\))f(and)i(\(8.8\))f(to)386 4529 y(deriv)m(e)1483 4540 y Fi(Z)1583 4566 y Fn(1)1539 4765 y Fj(1)1674 4675 y Fk(jh)p Fo(T)1798 4690 y Fj(2)1837 4675 y Fk(i)1876 4704 y Fm(t)1906 4675 y Fk(j)p Fo(dt)e(<)h Fk(1)p Fo(:)847 b Fp(\(8.15\))486 4869 y(F)-8 b(or)40 b(the)j(term)f Fo(T)1146 4884 y Fj(3)1227 4869 y Fp(w)m(e)h(compute)g (using)f(the)g(\014rst)h(iden)m(tit)m(y)g(of)f(\(8.13\))f(and)386 4985 y(\(3.11\))389 5265 y Fo(T)446 5280 y Fj(3)513 5265 y Fp(=)28 b(Re)748 5155 y Fi(\020)808 5265 y Fo(t)843 5224 y Fn(\000)p Fj(1)959 5239 y Fp(~)937 5265 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(g)1211 5184 y Fi(\000)1265 5265 y Fp(~)-58 b Fo(p)1305 5281 y Fn(jj)1349 5184 y Fi(\001)o(\000)1440 5265 y Fo(p)1489 5281 y Fn(jj)1555 5265 y Fk(\000)22 b Fo(t)1689 5224 y Fn(\000)p Fj(1)1784 5265 y Fo(r)1831 5184 y Fi(\001)1876 5265 y Fo(F)1939 5280 y Fn(\000)1998 5184 y Fi(\000)2044 5265 y Fo(C)2121 5224 y Fn(\000)p Fj(1)2215 5265 y Fo(t)2250 5224 y Fn(\000)p Fj(1)2345 5265 y Fo(r)2392 5184 y Fi(\001)2437 5265 y Fo(g)2488 5184 y Fi(\000)2541 5265 y Fp(~)-57 b Fo(p)2582 5281 y Fn(jj)2625 5184 y Fi(\001)2692 5239 y Fp(~)2671 5265 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))2894 5155 y Fi(\021)2976 5265 y Fp(+)22 b Fo(O)3152 5184 y Fi(\000)3197 5265 y Fo(t)3232 5224 y Fn(\000)p Fj(2)3326 5184 y Fi(\001)416 5460 y Fk(\024)29 b(\000)p Fo(\017t)673 5419 y Fn(\000)p Fj(1)789 5433 y Fp(~)768 5460 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(g)1042 5379 y Fi(\000)1095 5460 y Fp(~)-57 b Fo(p)1136 5475 y Fn(jj)1179 5379 y Fi(\001)1225 5460 y Fo(F)1288 5475 y Fn(\000)1347 5379 y Fi(\000)1393 5460 y Fo(C)1470 5419 y Fn(\000)p Fj(1)1564 5460 y Fo(t)1599 5419 y Fn(\000)p Fj(1)1694 5460 y Fo(r)1741 5379 y Fi(\001)1786 5460 y Fo(g)1837 5379 y Fi(\000)1890 5460 y Fp(~)g Fo(p)1931 5475 y Fn(jj)1974 5379 y Fi(\001)2041 5433 y Fp(~)2020 5460 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))21 b(+)h Fo(O)2441 5379 y Fi(\000)2486 5460 y Fo(t)2521 5419 y Fn(\000)p Fj(2)2616 5379 y Fi(\001)2661 5460 y Fp(;)17 b Fo(\017)28 b(>)g Fp(0)p Fo(:)173 b Fp(\(8.16\))486 5623 y(W)-8 b(e)33 b(conclude)h(\(8.9\))e(from)g(\(8.14\),)g(\(8.15\))g(and)g(\(8.16\).)p eop end %%Page: 36 36 TeXDict begin 36 35 bop 386 259 a Fl(36)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)486 459 y Fp(The)46 b(b)s(ound)f(\(8.10\))g(follo)m(ws)h(from)f(elemen)m(tary)i(energy)g(b) s(ounds,)i(T)-8 b(a)m(ylor)386 575 y(expansion)36 b(and)e(the)h (previous)h(estimates.)50 b(\(F)-8 b(or)34 b(this)h(w)m(e)g(need)g (\(8.9\))f(to)g(deal)386 691 y(with)27 b(the)f(\\region")g(where)h Fo(p)1471 655 y Fj(2)1471 721 y Fn(jj)1540 691 y Fp(energetically)h (has)f(the)f(righ)m(t)g(size,)j(but)d Fo(p)3086 707 y Fn(jj)3157 691 y Fo(<)i Fp(0.\))486 820 y(As)33 b(for)f(\(8.11\))g(w)m (e)h(consider)514 1072 y(\010\()p Fo(t)p Fp(\))28 b(=)848 1046 y(~)827 1072 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))s(~)-52 b Fo(g)1097 1087 y Fj(2)1136 991 y Fi(\000)1190 1072 y Fp(~)-57 b Fo(p)1231 1087 y Fn(jj)1274 991 y Fi(\001)1319 1072 y Fo(F)1396 991 y Fi(\000)1442 1072 y Fo(t)1477 1031 y Fn(\000)p Fj(1)1571 1072 y Fo(r)1618 991 y Fi(\001)1667 1072 y Fp(~)-52 b Fo(g)1711 1087 y Fj(2)1750 991 y Fi(\000)1804 1072 y Fp(~)-57 b Fo(p)1845 1087 y Fn(jj)1888 991 y Fi(\001)1955 1046 y Fp(~)1934 1072 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\);)114 b Fo(F)14 b Fp(\()p Fo(s)2459 1031 y Fn(0)2482 1072 y Fp(\))27 b(=)2651 936 y Fi(Z)2751 963 y Fm(s)2784 939 y Fc(0)2706 1162 y Fn(\0001)2852 1072 y Fo(g)2903 1031 y Fn(\000)2899 1097 y Fj(1)2962 1072 y Fp(\()p Fo(s)p Fp(\))3084 1024 y Fj(2)3123 1072 y Fo(ds:)386 1304 y Fp(W)-8 b(e)33 b(write)g(its)g(Heisen)m(b)s(erg)i(deriv)-5 b(ativ)m(e)34 b(as)863 1478 y FC(D)p Fp(\010\()p Fo(t)p Fp(\))28 b(=)g Fo(T)1319 1493 y Fj(1)1380 1478 y Fp(+)22 b Fo(T)1535 1493 y Fj(2)1575 1478 y Fp(;)863 1647 y Fo(T)920 1662 y Fj(1)987 1647 y Fp(=)1112 1621 y(~)1091 1647 y Fo(f)11 b Fp(\()o Fo(H)d Fp(\))1314 1566 y Fi(\000)1360 1647 y FC(D)s Fp(~)-52 b Fo(g)1493 1662 y Fj(2)1532 1566 y Fi(\000)1586 1647 y Fp(~)-58 b Fo(p)1626 1663 y Fn(jj)1670 1566 y Fi(\001)o(\001)1761 1647 y Fo(F)1838 1566 y Fi(\000)1883 1647 y Fo(t)1918 1606 y Fn(\000)p Fj(1)2013 1647 y Fo(r)2060 1566 y Fi(\001)2109 1647 y Fp(~)-53 b Fo(g)2152 1662 y Fj(2)2191 1566 y Fi(\000)2245 1647 y Fp(~)c Fo(p)2286 1663 y Fn(jj)2329 1566 y Fi(\001)2396 1621 y Fp(~)2375 1647 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))21 b(+)h Fo(h:c:;)863 1816 y(T)920 1831 y Fj(2)987 1816 y Fp(=)1112 1790 y(~)1091 1816 y Fo(f)11 b Fp(\()o Fo(H)d Fp(\))s(~)-52 b Fo(g)1361 1831 y Fj(2)1400 1735 y Fi(\000)1454 1816 y Fp(~)-57 b Fo(p)1495 1831 y Fn(jj)1538 1735 y Fi(\001\000)1629 1816 y FC(D)p Fo(F)1792 1735 y Fi(\000)1838 1816 y Fo(t)1873 1775 y Fn(\000)p Fj(1)1967 1816 y Fo(r)2014 1735 y Fi(\001\001)2109 1816 y Fp(~)k Fo(g)2152 1831 y Fj(2)2191 1735 y Fi(\000)2245 1816 y Fp(~)c Fo(p)2286 1831 y Fn(jj)2329 1735 y Fi(\001)2396 1790 y Fp(~)2375 1816 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(:)486 1996 y Fp(Using)26 b(\(8.4\),)g(\(8.5\),)h(the)e(second)i (iden)m(tit)m(y)h(of)d(\(8.13\))f(and)i(\(3.11\))f(as)g(for)g(\(8.9\)) 386 2112 y(w)m(e)34 b(obtain)e(that)1483 2140 y Fi(Z)1583 2166 y Fn(1)1539 2366 y Fj(1)1674 2276 y Fk(jh)p Fo(T)1798 2291 y Fj(1)1837 2276 y Fk(i)1876 2305 y Fm(t)1906 2276 y Fk(j)p Fo(dt)27 b(<)h Fk(1)p Fo(:)847 b Fp(\(8.17\))486 2486 y(As)34 b(for)f(the)h(the)g(term)g Fo(T)1410 2501 y Fj(2)1483 2486 y Fp(w)m(e)h(compute)f(using)h(the)f(\014rst)g(iden)m (tit)m(y)h(of)e(\(8.13\))386 2602 y(and)g(\(3.11\))570 2786 y Fo(T)627 2801 y Fj(2)694 2786 y Fp(=)28 b Fo(t)833 2745 y Fn(\000)p Fj(1)948 2760 y Fp(~)927 2786 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo(B)1229 2745 y Fn(\000)1288 2786 y Fp(\()p Fo(t)p Fp(\))1400 2737 y Fn(\003)1439 2705 y Fi(\000)1485 2786 y Fo(p)1534 2801 y Fn(jj)1599 2786 y Fk(\000)23 b Fo(t)1734 2745 y Fn(\000)p Fj(1)1828 2786 y Fo(r)1875 2705 y Fi(\001)1921 2786 y Fo(B)2000 2745 y Fn(\000)2059 2786 y Fp(\()p Fo(t)p Fp(\))2191 2760 y(~)2170 2786 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))21 b(+)h Fo(O)2591 2705 y Fi(\000)2636 2786 y Fo(t)2671 2745 y Fn(\000)p Fj(2)2766 2705 y Fi(\001)597 2977 y Fk(\025)29 b Fo(t)738 2936 y Fn(\000)p Fj(1)832 2977 y Fo(B)911 2936 y Fn(\000)970 2977 y Fp(\()p Fo(t)p Fp(\))1081 2928 y Fn(\003)1121 2866 y Fi(\020)1189 2977 y Fp(~)-58 b Fo(p)1229 2992 y Fn(jj)1273 2977 y Fp(1)1322 2992 y Fj([)r(~)-37 b Fm(c)1373 3001 y Fc(\000)1424 2992 y Fm(;)p Fn(1)p Fj(\))1546 2896 y Fi(\000)1599 2977 y Fp(~)-57 b Fo(p)1640 2992 y Fn(jj)1683 2896 y Fi(\001)1751 2977 y Fk(\000)23 b Fo(c)1893 2936 y Fn(\000)1893 3001 y Fj(+)1973 2951 y Fp(~)1952 2977 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))2175 2928 y Fj(2)2214 2866 y Fi(\021)2274 2977 y Fo(B)2353 2936 y Fn(\000)2412 2977 y Fp(\()p Fo(t)p Fp(\))22 b(+)g Fo(O)2721 2896 y Fi(\000)2766 2977 y Fo(t)2801 2936 y Fn(\000)p Fj(2)2896 2896 y Fi(\001)597 3164 y Fk(\025)29 b Fo(\017t)777 3122 y Fn(\000)p Fj(1)872 3164 y Fo(B)951 3122 y Fn(\000)1010 3164 y Fp(\()p Fo(t)p Fp(\))1121 3115 y Fn(\003)1160 3164 y Fo(B)1239 3122 y Fn(\000)1298 3164 y Fp(\()p Fo(t)p Fp(\))23 b(+)f Fo(O)1608 3083 y Fi(\000)1653 3164 y Fo(t)1688 3122 y Fn(\000)p Fj(2)1782 3083 y Fi(\001)1828 3164 y Fp(;)114 b Fo(\017)28 b Fp(=)i(~)-51 b Fo(c)2182 3179 y Fn(\000)2263 3164 y Fk(\000)22 b Fo(c)2404 3122 y Fn(\000)2404 3188 y Fj(+)2463 3164 y Fo(:)3125 2972 y Fp(\(8.18\))486 3344 y(Clearly)33 b(\(8.11\))f(follo)m(ws)h(b)m (y)h(com)m(bining)g(\(8.17\))d(and)i(\(8.18\).)486 3460 y(As)g(for)f(\(8.12\))g(w)m(e)h(ma)m(y)g(pro)s(ceed)h(similarly)g (using)514 3711 y(\010\()p Fo(t)p Fp(\))28 b(=)848 3685 y(~)827 3711 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))s(~)-52 b Fo(g)1097 3726 y Fj(2)1136 3631 y Fi(\000)1190 3711 y Fp(~)-57 b Fo(p)1231 3727 y Fn(jj)1274 3631 y Fi(\001)1319 3711 y Fo(F)1396 3631 y Fi(\000)1442 3711 y Fo(t)1477 3670 y Fn(\000)p Fj(1)1571 3711 y Fo(r)1618 3631 y Fi(\001)1667 3711 y Fp(~)-52 b Fo(g)1711 3726 y Fj(2)1750 3631 y Fi(\000)1804 3711 y Fp(~)-57 b Fo(p)1845 3727 y Fn(jj)1888 3631 y Fi(\001)1955 3685 y Fp(~)1934 3711 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\);)114 b Fo(F)14 b Fp(\()p Fo(s)2459 3670 y Fn(0)2482 3711 y Fp(\))27 b(=)2651 3576 y Fi(Z)2751 3602 y Fm(s)2784 3579 y Fc(0)2706 3801 y Fn(\0001)2852 3711 y Fo(g)2903 3670 y Fj(+)2899 3736 y(1)2962 3711 y Fp(\()p Fo(s)p Fp(\))3084 3663 y Fj(2)3123 3711 y Fo(ds:)3297 3942 y Fe(\003)386 4126 y FC(Corollary)38 b(8.2.)i Fg(L)-5 b(et)34 b Fo( )t Fg(,)g Fo(\037)1457 4141 y Fm(l)1511 4126 y Fk(2)28 b Fo(C)1682 4090 y Fn(1)1675 4150 y Fj(0)1757 4126 y Fp(\()p Fk(C)1847 4141 y Fm(\017)1880 4126 y Fp(\))33 b Fg(and)k Fp(~)-53 b Fo(g)2186 4141 y Fj(2)2259 4126 y Fg(b)-5 b(e)33 b(given)g(as)g(in)h(L)-5 b(emma)32 b(8.1.)386 4242 y(L)-5 b(et)37 b Fo(g)603 4257 y Fj(1)673 4242 y Fk(2)31 b Fo(C)847 4206 y Fn(1)840 4267 y Fj(0)922 4242 y Fp(\()p FC(R)p Fp(\))36 b Fg(b)-5 b(e)36 b(given)g(such)g(that)h Fp(0)31 b Fk(\024)g Fo(g)2154 4257 y Fj(1)2224 4242 y Fk(\024)h Fp(1)k Fg(and)g Fo(g)2656 4257 y Fj(1)2726 4242 y Fp(=)31 b(1)36 b Fg(in)g(an)g(op)-5 b(en)386 4358 y(interval)34 b(c)-5 b(ontaining)34 b Fp(supp)18 b(\()s(~)-52 b Fo(g)1522 4373 y Fj(2)1561 4358 y Fp(\))p Fg(.)44 b(Then)573 4542 y Fk(jj)p Fo( )t Fp(\()p Fo(t)p Fp(\))22 b Fk(\000)g Fo(g)975 4557 y Fj(1)1015 4461 y Fi(\000)1060 4542 y Fo(t)1095 4501 y Fn(\000)p Fj(1)1190 4542 y Fo(r)1237 4461 y Fi(\001)1286 4542 y Fp(~)-53 b Fo(g)1329 4557 y Fj(2)1368 4461 y Fi(\000)1422 4542 y Fp(~)c Fo(p)1463 4557 y Fn(jj)1506 4461 y Fi(\001)1552 4542 y Fo(\037)1613 4557 y Fm(l)1639 4542 y Fp(\()6 b(^)-55 b Fo(x)p Fp(\))1792 4516 y(~)1770 4542 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )t Fp(\()p Fo(t)p Fp(\))q Fk(jj)27 b(!)g Fp(0)35 b Fg(for)f Fo(t)28 b Fk(!)f(1)p Fo(:)187 b Fp(\(8.19\))386 4726 y Fg(Pr)-5 b(o)g(of.)41 b Fp(F)-8 b(rom)32 b(the)h(v)m(ery)h (de\014nition)g(of)e Fo( )k Fp(w)m(e)e(ha)m(v)m(e)1014 4904 y Fk(jj)p Fo( )t Fp(\()o Fo(t)p Fp(\))23 b Fk(\000)f Fo(\037)1430 4919 y Fm(l)1456 4904 y Fp(\()6 b(^)-55 b Fo(x)q Fp(\))1609 4878 y(~)1588 4904 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)27 b(!)g Fp(0)33 b(for)f Fo(t)27 b Fk(!)h(1)p Fo(:)386 5078 y Fp(Next,)33 b(from)g([H,)g(Theorems)h(4.10)e(and)h(4.12])f(w)m(e)h (learn)g(that)755 5262 y Fk(jj)p Fo( )t Fp(\()o Fo(t)p Fp(\))22 b Fk(\000)k Fp(~)-52 b Fo(g)1157 5277 y Fj(2)1196 5181 y Fi(\000)1250 5262 y Fp(~)-57 b Fo(p)1291 5277 y Fn(jj)1334 5181 y Fi(\001)1380 5262 y Fo(\037)1441 5277 y Fm(l)1467 5262 y Fp(\()6 b(^)-55 b Fo(x)p Fp(\))1619 5235 y(~)1598 5262 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)27 b(!)h Fp(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(:)368 b Fp(\(8.20\))386 5438 y(Whence)34 b(to)e(sho)m(w)i(\(8.19\))e(it)g(su\016ces)j(to)d(v)m(erify)i(that)708 5621 y Fk(jj)764 5540 y Fi(\010)821 5621 y Fo(g)868 5636 y Fj(1)907 5540 y Fi(\000)953 5621 y Fo(t)988 5580 y Fn(\000)p Fj(1)1082 5621 y Fo(r)1129 5540 y Fi(\001)1197 5621 y Fk(\000)23 b Fo(g)1344 5636 y Fj(1)1383 5540 y Fi(\000)1437 5621 y Fp(~)-58 b Fo(p)1477 5637 y Fn(jj)1521 5540 y Fi(\001)o(\011)1628 5621 y Fp(~)-53 b Fo(g)1671 5636 y Fj(2)1711 5540 y Fi(\000)1764 5621 y Fp(~)c Fo(p)1805 5637 y Fn(jj)1849 5540 y Fi(\001)1915 5595 y Fp(~)1894 5621 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)27 b(!)h Fp(0)k(for)g Fo(t)c Fk(!)f(1)p Fo(;)p eop end %%Page: 37 37 TeXDict begin 37 36 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(37)386 459 y Fp(whic)m(h)39 b(in)e(turn)g(is)h(reduced) g(\(b)m(y)g(a)f(standard)g(densit)m(y)i(argumen)m(t)f(using)g(that)386 575 y(the)f(energy)g(b)s(ounds)g(the)f(momen)m(tum\))i(to)e(v)m (erifying)i(that)e(for)f(all)h(constan)m(ts)386 691 y Fo(C)j Fp(large)33 b(enough)469 887 y Fk(jj)p Fo(F)588 902 y Fn(\000)646 807 y Fi(\000)692 887 y Fo(C)769 846 y Fn(\000)p Fj(1)863 887 y Fo(t)898 846 y Fn(\000)p Fj(1)993 887 y Fo(r)1040 807 y Fi(\001)o(\010)1143 887 y Fo(g)1190 902 y Fj(1)1230 807 y Fi(\000)1275 887 y Fo(t)1310 846 y Fn(\000)p Fj(1)1405 887 y Fo(r)1452 807 y Fi(\001)1519 887 y Fk(\000)23 b Fo(g)1666 902 y Fj(1)1705 807 y Fi(\000)1759 887 y Fp(~)-57 b Fo(p)1800 903 y Fn(jj)1843 807 y Fi(\001\011)1950 887 y Fp(~)-52 b Fo(g)1994 902 y Fj(2)2033 807 y Fi(\000)2087 887 y Fp(~)-57 b Fo(p)2128 903 y Fn(jj)2171 807 y Fi(\001)2238 861 y Fp(~)2217 887 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))p Fo( )t Fp(\()p Fo(t)p Fp(\))p Fk(jj)2373 1038 y(!)27 b Fp(0)g(for)32 b Fo(t)c Fk(!)g(1)p Fo(:)82 b Fp(\(8.21\))486 1207 y(F)-8 b(or)31 b(\(8.21\))h(w)m(e)i(consider)g(the)f(observ)-5 b(able)469 1399 y(\010)539 1414 y Fm(C)599 1399 y Fp(\()o Fo(t)p Fp(\))532 1577 y(=)657 1551 y(~)636 1577 y Fo(f)10 b Fp(\()p Fo(H)e Fp(\))s(~)-52 b Fo(g)906 1592 y Fj(2)945 1496 y Fi(\000)999 1577 y Fp(~)-57 b Fo(p)1040 1592 y Fn(jj)1083 1496 y Fi(\001)1129 1577 y Fo(F)1192 1592 y Fn(\000)1251 1496 y Fi(\000)1296 1577 y Fo(C)1373 1536 y Fn(\000)p Fj(1)1468 1577 y Fo(t)1503 1536 y Fn(\000)p Fj(1)1597 1577 y Fo(r)1644 1496 y Fi(\001\000)1744 1577 y Fp(~)f Fo(p)1784 1592 y Fn(jj)1850 1577 y Fk(\000)22 b Fo(t)1984 1536 y Fn(\000)p Fj(1)2079 1577 y Fo(r)2126 1496 y Fi(\001)2171 1519 y Fj(2)2211 1577 y Fo(F)2274 1592 y Fn(\000)2333 1496 y Fi(\000)2379 1577 y Fo(C)2456 1536 y Fn(\000)p Fj(1)2550 1577 y Fo(t)2585 1536 y Fn(\000)p Fj(1)2679 1577 y Fo(r)2726 1496 y Fi(\001)2775 1577 y Fp(~)-52 b Fo(g)2819 1592 y Fj(2)2858 1496 y Fi(\000)2912 1577 y Fp(~)-58 b Fo(p)2952 1592 y Fn(jj)2996 1496 y Fi(\001)3063 1551 y Fp(~)3041 1577 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(:)486 1740 y Fp(Using)34 b(Lemma)g(8.1)f(as)h(w)m (ell)g(as)g(the)g(pro)s(of)f(of)g(this)h(lemma)g(w)m(e)h(easily)g(sho)m (w)386 1857 y(that)883 1871 y Fi(\014)883 1931 y(\014)883 1991 y(\014)883 2050 y(\014)916 1880 y(Z)1016 1906 y Fn(1)972 2106 y Fj(1)1107 2016 y Fk(j)1162 1948 y Fo(d)p 1145 1993 86 4 v 1145 2084 a(dt)1241 2016 y Fk(h)o Fp(\010)1349 2031 y Fm(C)1409 2016 y Fp(\()p Fo(t)p Fp(\))p Fk(i)1559 2045 y Fm(t)1588 1871 y Fi(\014)1588 1931 y(\014)1588 1991 y(\014)1588 2050 y(\014)1638 2016 y Fo(dt;)1865 1880 y Fi(Z)1965 1906 y Fn(1)1921 2106 y Fj(1)2056 2016 y Fo(t)2091 1974 y Fn(\000)p Fj(1)2186 2016 y Fk(h)p Fp(\010)2295 2031 y Fm(C)2354 2016 y Fp(\()p Fo(t)p Fp(\))p Fk(i)2504 2045 y Fm(t)2534 2016 y Fo(dt)27 b(<)h Fk(1)p Fo(;)386 2214 y Fp(from)46 b(whic)m(h)i(w)m(e)g(conclude)g(that)e (along)g(some)i(sequence)h Fo(t)2707 2229 y Fm(k)2801 2214 y Fk(!)i(1)46 b Fp(indeed)386 2330 y Fk(h)p Fp(\010)495 2345 y Fm(C)554 2330 y Fp(\()p Fo(t)627 2345 y Fm(k)670 2330 y Fp(\))p Fk(i)747 2360 y Fm(t)772 2372 y Ff(k)842 2330 y Fk(!)27 b Fp(0,)33 b(and)g(then)g(in)g(turn)f(that)1591 2501 y Fk(h)p Fp(\010)1700 2516 y Fm(C)1759 2501 y Fp(\()p Fo(t)p Fp(\))p Fk(i)1909 2530 y Fm(t)1966 2501 y Fk(!)c Fp(0)p Fo(:)955 b Fp(\(8.22\))486 2664 y(W)-8 b(e)33 b(easily)g(obtain)g(\(8.21\))f(using)h(\(8.22\),)f(\(3.10\))g(and)g (comm)m(utation.)167 b Fe(\003)486 2838 y Fp(No)m(w,)42 b(one)e(ma)m(y)g(easily)h(v)m(erify)g(\(8.2\))e(for)h Fo( )j Fp(=)d Fo(P)2384 2853 y Fm(l)2410 2838 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))o Fo( )44 b Fp(as)c(follo)m(ws:)58 b(W)-8 b(e)386 2954 y(in)m(tro)s(duce)40 b(a)g(partition)f Fo(f)50 b Fp(=)1542 2879 y Fi(P)1663 2954 y Fo(f)1711 2969 y Fm(i)1779 2954 y Fp(of)39 b(sharply)i(lo)s(calized)f Fo(f)2702 2969 y Fm(i)2730 2954 y Fp(`s)g(and)g(for)f(eac)m(h)386 3080 y(of)k(these)h(a)f(\\sligh)m(tly)h(larger")1618 3054 y(~)1597 3080 y Fo(f)1645 3095 y Fm(i)1673 3080 y Fp(.)75 b(Using)44 b(these)g(functions)g(and)f(the)h(states)386 3196 y Fo( )449 3211 y Fm(i)510 3196 y Fp(=)32 b Fo(P)681 3211 y Fm(l)707 3196 y Fo(f)755 3211 y Fm(i)783 3196 y Fp(\()p Fo(H)8 b Fp(\))o Fo( )39 b Fp(as)d(input)g(in)f(Corollary)g (8.2)g(the)h(b)s(ounds)g(\(1.8\))e(follo)m(w)i(from)386 3312 y(the)k(conclusion)g(of)f(the)h(corollary)g(and)f([H,)h(Theorems)h (4.10)d(and)i(4.12].)63 b(As)386 3428 y(for)36 b(\(1.9\))f(w)m(e)j(ma)m (y)f(use)g(the)g(same)g(partition)f(and)g(then)h(conclude)h(the)f (result)386 3554 y(from)32 b(Lemma)h(8.1)g(\(applied)g(with)1744 3528 y(~)1723 3554 y Fo(f)43 b Fp(replaced)34 b(b)m(y)2356 3528 y(~)2335 3554 y Fo(f)2383 3569 y Fm(i)2443 3554 y Fp(\).)386 3732 y Fg(R)-5 b(emarks)42 b Fp(8.3)p Fg(.)534 3872 y Fp(\(1\))f(Using)36 b(the)g(Mourre)g(estimate)h([A)m(CH,)f (Theorem)h(C.1])f(one)f(ma)m(y)i(eas-)700 3990 y(ily)f(include)g(a)e (short-range)h(p)s(erturbation)g Fo(V)2411 4005 y Fj(1)2482 3990 y Fp(=)c Fo(O)2667 3909 y Fi(\000)2712 3990 y Fk(j)p Fo(x)p Fk(j)2823 3953 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\016)3005 3909 y Fi(\001)3051 3990 y Fp(,)k Fo(\016)h(>)31 b Fp(0,)700 4112 y Fo(@)756 4076 y Fm(\013)751 4136 y(x)807 4112 y Fo(V)864 4127 y Fj(1)947 4112 y Fp(=)44 b Fo(O)s Fp(\()o Fk(j)p Fo(x)p Fk(j)1293 4076 y Fn(\000)p Fj(2)1387 4112 y Fp(\),)g Fk(j)p Fo(\013)q Fk(j)f Fp(=)h(2,)g(to)d(the)i(Hamiltonian)f Fo(H)8 b Fp(.)72 b(In)42 b(partic-)700 4228 y(ular)j(Theorem)h(1.2)e (holds)h(for)f(the)h(strictly)h(homogeneous)g(case)f(as)700 4344 y(discussed)36 b(in)d(Section)g(1.)534 4460 y(\(2\))41 b(The)25 b(non-degeneracy)g(condition)f(at)f Fo(!)2164 4475 y Fm(l)2213 4460 y Fp(is)h(imp)s(ortan)m(t)f(for)g(the)h(metho)s (d)700 4577 y(of)38 b(pro)s(of)f(presen)m(ted)k(in)d(this)h(pap)s(er.) 60 b(Ho)m(w)m(ev)m(er)40 b(it)e(is)h(not)f(imp)s(ortan)m(t)700 4693 y(that)47 b(the)f(set)h(of)f(critical)h(p)s(oin)m(ts)g Fo(C)2114 4708 y Fm(r)2198 4693 y Fp(is)f(\014nite;)54 b(it)47 b(su\016ces)h(that)e Fo(!)3349 4708 y Fm(l)700 4809 y Fp(is)41 b(an)e(isolated)i(non-degenerate)f(critical)g(p)s(oin)m (t)g(and)g(that)f Fo(V)22 b Fp(\()p Fo(C)3194 4824 y Fm(r)3232 4809 y Fp(\))39 b(is)700 4925 y(coun)m(table.)534 5042 y(\(3\))i(A)m(t)46 b(a)f(lo)s(cal)g(maxim)m(um)i(w)m(e)f(pro)m(v)m (ed)g(a)f(somewhat)i(b)s(etter)e(result)h(in)700 5158 y([HS1])37 b(\(b)m(y)h(a)e(di\013eren)m(t)i(metho)s(d\):)53 b(A)36 b(larger)h(class)h(of)e(p)s(erturbations)700 5274 y(w)m(as)50 b(included)g(and)e(w)m(e)h(imp)s(osed)h(a)d(somewhat)j(w)m (eak)m(er)g(condition)700 5390 y(than)22 b(the)g(non-degeneracy)i (condition.)40 b(The)23 b(metho)s(d)f(of)f([HS1])h(yielded)700 5506 y(only)32 b(a)g(limited)g(result)h(at)e(saddle)h(p)s(oin)m(ts.)44 b(Although)32 b(there)g(are)g(indi-)700 5623 y(cations)25 b(that)f(this)h(metho)s(d)g(of)f(pro)s(of)f(migh)m(t)i(b)s(e)g (extended)h(to)e(included)p eop end %%Page: 38 38 TeXDict begin 38 37 bop 386 259 a Fl(38)755 b(IRA)24 b(HERBST)i(AND)e(ERIK)h(SKIBSTED)700 459 y Fp(Theorem)34 b(1.2)d(\(b)m(y)h(using)h(a)e(certain)i(complicated)g(iteration)e(sc)m (heme\))700 575 y(the)i(pro)s(of)f(presen)m(ted)j(in)e(this)g(pap)s(er) g(is)g(probably)g(m)m(uc)m(h)h(simpler.)534 691 y(\(4\))41 b(The)34 b(comp)s(onen)m(ts)g(of)e(the)h Fo(\015)38 b Fp(of)h(\(2.3\))32 b(ma)m(y)h(b)s(e)g(tak)m(en)g(of)g(the)g(form)1144 900 y Fo(\015)1195 915 y Fm(j)1258 900 y Fp(=)28 b Fo(\021)1410 915 y Fm(j)1469 900 y Fp(+)1567 810 y Fi(p)p 1666 810 566 4 v 1666 900 a Fp(2\()p Fo(E)g Fk(\000)23 b Fo(V)e Fp(\()p Fo(!)2130 915 y Fm(l)2156 900 y Fp(\)\))p Fo(\014)2293 852 y Fj(#)2287 925 y Fm(j)2355 900 y Fp(\()p Fo(E)6 b Fp(\))p Fo(u)2565 915 y Fm(j;)700 1117 y Fp(where)46 b Fo(\014)1055 1070 y Fj(#)1049 1142 y Fm(j)1118 1117 y Fp(\()p Fo(E)6 b Fp(\))44 b(is)h(giv)m(en)h(b)m(y)g(one)f(of)f(the)h (expressions)i(of)d(\(8.1\).)79 b(In)700 1238 y(particular)31 b(b)s(oth)e(of)h(the)g(conditions)h(\(2.8\))f(and)g(\(2.9\))f(are)h (satis\014ed)h(in)700 1355 y(the)i(p)s(oten)m(tial)g(case.)534 1471 y(\(5\))41 b(W)-8 b(e)43 b(applied)g(the)g(Stern)m(b)s(erg)g (linearization)g(pro)s(cedure)h(in)e([HS2])h(to)700 1587 y(the)30 b(equations)h(\(1.6\))e(in)h(the)g(case)g(of)f(a)g(lo)s(cal)h (minim)m(um.)44 b(In)30 b(this)g(case)700 1703 y(the)e(union)g(of)f (all)g(resonances)j(\(of)d(all)g(orders)h(and)g(for)e(all)i(eigen)m(v) -5 b(alues\))700 1820 y(is)49 b(discrete)h(on)f(\()p Fo(V)21 b Fp(\()p Fo(!)1555 1835 y Fm(l)1581 1820 y Fp(\))p Fo(;)c Fk(1)p Fp(\))o(.)91 b(One)49 b(needs)h(to)e(exclude)i(this)f (set)g(of)700 1936 y(resonances)25 b(to)e(construct)h(a)e(smo)s(oth)h (Stern)m(b)s(erg)h(di\013eomorphism,)j(see)700 2052 y(for)40 b(example)i([N,)f(Theorem)g(9].)67 b(The)41 b(construction)h(of)e(the)g (sym)m(b)s(ol)700 2171 y Fo(\015)756 2135 y Fj(\()q Fm(m)p Fj(\))914 2171 y Fp(in)c(\(2.18\))f(ma)m(y)h(b)s(e)g(view)m(ed)i(as)e (a)g(rudimen)m(t)h(of)e(this)i(pro)s(cedure.)700 2287 y(Ho)m(w)m(ev)m(er,)49 b(the)44 b(union)g(of)f(all)h(resonances)h(at)e (a)g(lo)s(cal)h(maxim)m(um)h(or)700 2404 y(a)d(saddle)g(p)s(oin)m(t)g Fo(!)1423 2419 y Fm(l)1490 2404 y Fp(is)g(dense)h(in)f(\()p Fo(V)22 b Fp(\()o Fo(!)2210 2419 y Fm(l)2236 2404 y Fp(\))p Fo(;)17 b Fk(1)p Fp(\))o(,)44 b(and)e(for)f(that)g(reason)700 2520 y(the)23 b(smo)s(oth)f(Stern)m(b)s(erg)g(di\013eomorphism)i (\(de\014ned)f(at)f(non-resonance)700 2636 y(energies\))41 b(w)m(ould)f(not)f(b)s(e)h(suited)g(for)f(quan)m(tization.)64 b(Although)40 b(not)700 2755 y(elab)s(orated,)33 b(one)g(ma)m(y)g (essen)m(tially)i(view)f Fo(\015)2345 2719 y Fj(\()p Fm(m)p Fj(\))2499 2755 y Fp(as)e(b)s(eing)h(constructed)700 2872 y(b)m(y)h(a)e Fo(C)994 2835 y Fm(m)1093 2872 y Fp(Stern)m(b)s(erg) i(di\013eomorphism.)1590 3174 y Fq(References)386 3331 y FB([A)n(CH])69 b(S.)32 b(Agmon,)g(J.)f(Cruz,)h(I.)f(Herbst:)89 b Fb(Gener)l(alize)l(d)35 b(F)-6 b(ourier)33 b(tr)l(ansform)g(for)h (Schr\177)-42 b(o-)683 3431 y(dinger)25 b(op)l(er)l(ators)f(with)g(p)l (otentials)g(of)h(or)l(der)f(zer)l(o,)f FB(J.)d(F.)h(A.,)i(167)c (\(1999\),)i(345{369.)386 3531 y([A1])147 b(V.)33 b(Arnold:)93 b Fb(Ge)l(ometric)l(al)35 b(Metho)l(ds)h(in)e(the)g(The)l(ory)h(of)g (Or)l(dinary)g(Di\013er)l(ential)683 3630 y(Equations,)29 b FB(Springer-V)-7 b(erlag,)25 b(New)j(Y)-7 b(ork,)27 b(1983.)386 3730 y([A2])147 b(V.)25 b(Arnold:)72 b Fb(Mathematic)l(al) 29 b(Metho)l(ds)g(of)f(Classic)l(al)h(Me)l(chanics,)e FB(2nd)e(ed.,)g(Sprin-)683 3829 y(ger-V)-7 b(erlag,)26 b(New)h(Y)-7 b(ork,)27 b(1989.)386 3929 y([C])191 b(M.P)-7 b(.)28 b(do)f(Carmo:)37 b Fb(R)n(iemannian)30 b(Ge)l(ometry,)f FB(Birkh\177)-42 b(auser,)26 b(Boston,)g(1992.)386 4029 y([CHS1])41 b(H.)28 b(Cornean,)e(I.)h(Herbst,)g(E.)f(Skibsted:)75 b Fb(Spir)l(aling)31 b(attr)l(actors)e(and)g(quantum)f(dy-)683 4128 y(namics)f(for)g(a)g(class)f(of)h(long-r)l(ange)g(magnetic)f (\014elds,)g FB(MaPh)n(ySto)c(preprin)n(t)h(no.)h(36)683 4228 y(No)n(v)n(em)n(b)r(er)j(2002.)386 4328 y([CHS2])41 b(H.)30 b(Cornean,)e(I.)h(Herbst,)h(E.)f(Skibsted:)81 b Fb(Classic)l(al)33 b(and)e(quantum)f(dynamics)j(for)683 4427 y FB(2)p Fz(D)r Fb({ele)l(ctr)l(omagnetic)h(p)l(otentials)g (asymptotic)l(al)t(ly)h(homo)l(gene)l(ous)f(of)g(de)l(gr)l(e)l(e)f(zer) l(o,)683 4527 y FB(in)28 b(preparation.)386 4626 y([D])188 b(J.)19 b(Derezi)r(\023)-44 b(nski:)66 b Fb(Asymptotic)22 b(c)l(ompleteness)h(for)f Fz(N)9 b Fb(-p)l(article)23 b(long-r)l(ange)f(quantum)683 4726 y(systems,)28 b FB(Ann.)h(Math.,)e (138)g(\(1993\),)f(427{476.)386 4826 y([DG])123 b(J.)31 b(Derezi)r(\023)-44 b(nski,)31 b(C.)f(G)n(\023)-39 b(erard:)84 b Fb(Sc)l(attering)32 b(the)l(ory)i(of)f(classic)l(al)h(and)f(quantum)e Fz(N)9 b Fb(-)683 4925 y(p)l(article)23 b(systems)p FB(,)d(T)-7 b(exts)18 b(and)h(Monographs)d(in)i(Ph)n(ysics,)h(Springer-V)-7 b(erlag,)18 b(Berlin,)683 5025 y(1997.)386 5125 y([F])197 b(G.B.)25 b(F)-7 b(olland:)72 b Fb(Harmonic)28 b(analysis)h(in)e(phase) h(sp)l(ac)l(e,)f FB(Annals)e(of)f(Mathematical)683 5224 y(studies,)k(122,)e(Princeton)h(Univ)n(ersit)n(y)g(Press,)f(Princeton,) g(1989.)386 5324 y([G1])144 b(C.)39 b(G)n(\023)-39 b(erard:)113 b Fb(Sharp)40 b(pr)l(op)l(agation)h(estimates)f(for)g Fz(N)9 b Fb({p)l(article)41 b(systems,)g FB(Duk)n(e)683 5423 y(Math.)28 b(J.,)g(67,)e(3)i(\(1992\),)e(483{515.)386 5523 y([G2])144 b(C.)45 b(G)n(\023)-39 b(erard:)139 b Fb(Asymptotic)47 b(c)l(ompleteness)f(for)g(3{p)l(articles)i(systems,)h FB(In)n(v)n(en)n(t.)683 5623 y(Math.)28 b(114)e(\(1993\),)h(333{397.)p eop end %%Page: 39 39 TeXDict begin 39 38 bop 1235 259 a Fl(ABSENCE)33 b(OF)g(QUANTUM)g(ST)-6 b(A)g(TES)771 b(39)386 459 y FB([GS])140 b(V.)29 b(Guillemin,)h(D.)f (Sc)n(hae\013er:)78 b Fb(On)30 b(a)h(c)l(ertain)g(class)g(of)h(F)-6 b(uchsian)31 b(p)l(artial)h(di\013er-)683 558 y(ential)f(e)l(quations,) d FB(Duk)n(e)g(Math.)f(J.,)h(44)f(\(1977\),)f(157{199.)386 658 y([HMV])51 b(A.)20 b(Hassell,)g(R.)f(Melrose,)h(A.)f(V)-7 b(asy:)66 b Fb(Sp)l(e)l(ctr)l(al)22 b(and)g(sc)l(attering)g(the)l(ory)h (for)f(symb)l(olic)683 758 y(p)l(otentials)31 b(of)f(or)l(der)h(zer)l (o)p FB(,)d(to)f(app)r(ear)g(in)h(Adv.)g(Math.)386 857 y([H])189 b(I.)34 b(Herbst:)97 b Fb(Sp)l(e)l(ctr)l(al)35 b(and)h(sc)l(attering)f(the)l(ory)g(for)h(Schr\177)-42 b(odinger)37 b(op)l(er)l(ators)f(with)683 957 y(p)l(otentials)31 b(indep)l(endent)f(of)h Fw(j)p Fz(x)p Fw(j)p Fb(,)e FB(Amer.)e(J.)h (Math.,)f(113)g(no.)g(3)g(\(1991\),)f(509{565.)386 1056 y([HS1])101 b(I.)38 b(Herbst,)h(E.)e(Skibsted:)112 b Fb(Quantum)37 b(sc)l(attering)i(for)g(homo)l(gene)l(ous)h(of)f(de)l(gr) l(e)l(e)683 1156 y(zer)l(o)g(p)l(otentials:)57 b(A)n(bsenc)l(e)39 b(of)g(channels)g(at)g(lo)l(c)l(al)g(maxima)g(and)h(sadd)t(le)g(p)l (oints,)683 1256 y FB(MaPh)n(ySto)27 b(preprin)n(t)g(no.)g(24)g(August) h(1999,)d(unpublished)k(man)n(uscript.)386 1355 y([HS2])101 b(I.)39 b(Herbst,)j(E.)d(Skibsted:)119 b Fb(Quantum)38 b(sc)l(attering)i(for)h(p)l(otentials)g(indep)l(endent)683 1455 y(of)e Fw(j)p Fz(x)p Fw(j)p Fb(:)54 b(Asymptotic)38 b(c)l(ompleteness)g(for)h(high)f(and)g(low)h(ener)l(gies,)g FB(to)d(app)r(ear)f(in)683 1555 y(Comm.)28 b(PDE.)386 1654 y([H\177)-42 b(o])147 b(L.)25 b(H\177)-42 b(ormander:)71 b Fb(The)28 b(analysis)g(of)g(p)l(artial)h(di\013er)l(ential)f(op)l(er) l(ators)g(III,)d FB(Springer-)683 1754 y(V)-7 b(erlag,)27 b(Berlin,)g(1985.)386 1857 y([M])691 1836 y(\023)683 1857 y(E.)32 b(Mourre:)89 b Fb(A)n(bsenc)l(e)33 b(of)h(singular)g(c)l (ontinuous)f(sp)l(e)l(ctrum)g(for)h(c)l(ertain)g(self-ad-)683 1957 y(joint)d(op)l(er)l(ators,)g FB(Comm)n(un.)c(Math.)h(Ph)n(ys.,)f (91)g(\(1981\),)f(391{408.)386 2056 y([M\034])133 b(J.S.)32 b(M\034ller:)88 b Fb(A)n(n)33 b(abstr)l(act)g(r)l(adiation)i(c)l (ondition)f(and)g(applic)l(ations)h(to)f Fz(N)9 b Fb({b)l(o)l(dy)683 2156 y(systems,)28 b FB(Rev.)g(Math.)g(Ph)n(ys.,)e(12)h(no.)g(5)h (\(2000\),)e(767{803.)386 2255 y([N])189 b(E.)24 b(Nelson:)71 b Fb(T)-6 b(opics)27 b(in)f(dynamics)i(I,)e(Flows,)g FB(Princeton)d(U.)h(Press)e(and)h(U.)h(T)-7 b(oky)n(o)683 2355 y(Press,)27 b(Princeton,)f(1969.)386 2455 y([RS])144 b(M.)23 b(Reed,)h(B.)e(Simon:)70 b Fb(F)-6 b(ourier)26 b(analysis,)h(self-adjointness.)g(Metho)l(ds)g(of)e(mo)l(dern)683 2554 y(mathematic)l(al)32 b(physics)f Fz(I)7 b(I)g Fb(,)28 b FB(Academic)g(Press,)e(New)i(Y)-7 b(ork,)27 b(1975.)386 2654 y([S1])163 b(E.)36 b(Skibsted:)107 b Fb(L)l(ong-r)l(ange)37 b(sc)l(attering)g(of)h(thr)l(e)l(e-b)l(o)l(dy)g(quantum)e(systems,)j (As-)683 2754 y(ymptotic)31 b(c)l(ompleteness,)e FB(In)n(v)n(en)n(t.)e (Math.)h(151)e(\(2003\),)g(65{99.)386 2853 y([S2])163 b(E.)39 b(Skibsted:)120 b Fb(L)l(ong-r)l(ange)40 b(sc)l(attering)h(of)g (thr)l(e)l(e-b)l(o)l(dy)g(quantum)e(systems,)k(II,)683 2953 y FB(Ann.)29 b(Henri)e(P)n(oincar)n(\023)-39 b(e,)25 b(4)i(\(2003\),)f(1{25.)486 3140 y(\(I.)20 b(Herbst\))g FA(Dep)-6 b(ar)g(tment)24 b(of)g(Ma)-6 b(thema)g(tics,)26 b(University)d(of)g(Vir)n(ginia,)h(Char-)386 3239 y(lottesville,)30 b(V)-10 b(A)31 b(22903,)f(U.S.A.)486 3339 y Fb(E-mail)g(addr)l(ess)7 b FB(:)38 b Fa(iwh@weyl.math.vir)o(gi)o(nia)o(.e)o(du)486 3508 y FB(\(E.)31 b(Skibsted\))g FA(Institut)k(f)n(or)h(Ma)-6 b(tema)g(tiske)36 b(F)-10 b(a)n(g,)37 b(Aarhus)d(Universitet,)i(Ny)386 3608 y(Munkegade)c(8000)f(Aarhus)f(C,)h(Denmark)486 3708 y Fb(E-mail)f(addr)l(ess)7 b FB(:)38 b Fa(skibsted@imf.au.d)o(k)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0310280251113--