Content-Type: multipart/mixed; boundary="-------------0512221319688" This is a multi-part message in MIME format. ---------------0512221319688 Content-Type: text/plain; name="05-436.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-436.keywords" quantum statistical mechanics, operator algebras, cyclic thermodynamic processes, Floquet theory ---------------0512221319688 Content-Type: application/postscript; name="cyclic.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="cyclic.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: cyclic.dvi %%Pages: 39 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMSY10 CMBX10 CMR10 CMBX12 CMSY7 CMTI10 %%+ CMMI12 CMR8 CMMI8 CMTI12 CMSY8 CMR7 CMBX8 CMEX10 CMR6 CMMI6 CMSY6 %%+ CMMI10 CMMI7 MSAM10 CMMI5 CMR5 TeX-cmex8 CMSS12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips cyclic.dvi %DVIPSParameters: 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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 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 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 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 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 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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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: 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 18 /parenleftbigg put dup 19 /parenrightbigg put dup 40 /braceleftBigg put dup 73 /contintegraldisplay put dup 77 /circleplusdisplay put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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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 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 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 0 /.notdef put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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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 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C BFB7C8C77C22A01C345078D28D3ECBF804CDC2FE5025FA0D05CCC5EFC0C4F87E CBED13DDDF8F34E404F471C6DD2E43331D73E89BBC71E7BF889F6293793FEF5A C9DD3792F032E37A364C70914843F7AA314413D022AE3238730B420A7E9D0CF5 D0E24F501451F9CDECE10AF7E14FF15C4F12F3FCA47DD9CD3C7AEA8D1551017D 23131C09ED104C052054520268A4FA3C6338BA6CF14C3DE3BAF2EA35296EE3D8 D6496277E11DFF6076FE64C8A8C3419FA774473D63223FFA41CBAE609C3D976B 93DFB4079ADC7C4EF07303F93808DDA9F651F61BCCF79555059A44CBAF84A711 6D98083CEF58230D54AD486C74C4A257FC703ACF918219D0A597A5F680B606E4 EF94ADF8BF91A5096A806DB64EC96636A98397D22A74932EB7346A9C4B5EE953 CB3C80AA634BFC28AA938C704BDA8DC4D13551CCFE2B2784BE8BF54502EBA9AF D49B79237B9C56310550BC30E9108BB06EAC755D6AA4E688EFE2A0AAB17F20FE 00CD0BFF1B9CB6BDA0FA3A29A3117388B6686657A150CE6421FD5D420F4F7FB5 B0DAA1BA19D638676E9CF159AC7325EF17B9F74E082BEF75E10A31C7011C0FFA 99B797CE549B5C45238DD0FADD6B99D233AC69282DF0D91EA2DBD08CE0083904 A6D968D5AE3BD159D01BDFF42D16111BC0A517C66B43972080D9DD4F3B9AE7FB 11B035CE715C1218B2D779761D8D7E9DEBE277531BD58F313EBD27E33BEF9DC5 50C7821A8BBC3B9FDF899D7EAA0B94493B97AFEAC503EB5ED7A7AB6CCCC950AF F6A29F479A2D64381EEF89EDD5DCD702BA9B4F7894BC1F1D150193DD6D1E88E8 B624CA11D98DBEC5110F3D4CE4C54DB5A07BFC4E4551AD1888E5C003F7C5B9C2 0052591BA569C0BFBF9B14804EB48E58CCABCE011D4C64DB95829FC036B3C447 E06601E68CEF8D21568FFBEBBE52938D76060A3D56544DCDAD0D7D0355677FAC 54D57BB954408BFD30481C13663CFDF9C0754517C4456F8093A2D97F834A62AF 19FB2298B8EC37A4AAC77D94CF45708393FD61264AB30A51FE00A87EA8CD624A 321F138240C9B8388CB7E347B9D41DB7E2A4E8202B27CB0407F9A19686082700 5BAC805EABC3058EC3CEE5AE3438AB86263DFE6100DCA23A3877222FFB51249E 2EE5AC0A516FB0BC42BF84D1E9A24A5DB59CCE51CA4239F68AB0F1F2C3285892 9A0C9A32B4275A324634F06028403E87A89D931B020FFE7774D6288271C49585 3060E6EEC494D2E2002E6132E809E57BEA9D8304FFF95EB55B300AF7C8FAB8C5 1E1ECFFACF425EB4BAA8ABC3E2C30F4110BF31AC1C82F84819AEA7DA74726E0F 658FB8AFEA3E5CDD3EE5B1F65F5ED0C3D145E1825319E19352BE65479AE3918E 16D7C2C3C6F5250F2F8813BF862D4223948BEBD25615506E4A57F6EDEF1C19DA D2603A876960971A5B9BDDF91B17243D531875603FD1F0BA4A1F1CD49669AEAB 5284AE7B76FEA05C823005AECCC1965BF8786D12B0D8155C61EAF583C49C4DC3 708DDF17DD99A98A706E2A5BBCF1FEF4F8D0F666A5F293843108AFABE686C946 381B947EC5356DCFFC9F4D6BF6FA8BE046F1A06866794CE424E19CBB180C4CE1 630014198960F2F2E23E9AE274A0A942DAEE793E7DDA9B452291903B34B708C0 7954CB70ECF7F18BC7BD8E559838F1C5CD50C49EAEEFEFCB244DBF920BB75FAF 109680DBD408DBC6CADBF5780831B91B34AD9C34F6D049423E342E84D39BB36E 91741ED27C61C4679CB0A3CAF30C092D4FC7A8B5F6017E03D4298BCF458CDFB5 47448E23809F5B533B4C762BE2BDB34894AB88885F554EA59B89AF642B1C1BDD C54B2F01CA6CFD1672DF804194755DC75C9DD5857A0180E4943903F92247D94D 805E66A8A99B6CC1D4B7139701F727ECC68E993EB7AF0BD792EEF0A781F4D77F 2641675733659B2761DE7A6B3590A73A2DD2F7A34E62797507D31980C65756DA 7DFA896E145EB0B96FCA178E022207CBA7367EF190600D53D01A614C9364E5F9 3F0B383C84441F6F6EAE939BAA3020AC25B71B6C3998E7992E26FCC2EA3A6915 C4C71179AC6132CDF234BD06B37FF6DFCB71BAFCDA6B5A682A3EC40CDC8CC7D4 ED743AFD0B0E51E933521C7B5403C65D0F7378CABEB4AAFF935899F940097B27 2667A4F86D588A6D6AFEF0F314688A8956010742CFE85966F514B99AA4AAFB1B 9ECD4039BF32C12FA6CCF8DFD8C1A9F585533F61472BAA47095411CB8B828D51 97CC690D42486393A794EADEE9242E6DE85F087CA75ABE9C8712B90E 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 0 /.notdef put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec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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 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. 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0000000000000000000000000000000000000000000000000000000000000000 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. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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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 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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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 /.notdef put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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. 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y(op)s(erator.)82 b(Hence)48 b Fy(K)1188 3077 y Ft(\003)1181 3138 y Fv(g)1227 3113 y FB(\()p Fy(t;)17 b(\022)s FB(\))46 b(is)g(w)m(ell-de\014ned)j(and)d(closed)h(on)e(the)i (domain)f Fx(D)53 b FB(:=)324 3234 y Fx(D)s FB(\()p Fy(i@)526 3249 y Fv(t)556 3234 y FB(\))18 b Fx(\\)h(D)s FB(\()p Fy(N)10 b FB(\))19 b Fx(\\)g(D)s FB(\()p Fx(L)1232 3197 y Ft(R)1292 3206 y Fn(1)1330 3234 y FB(\))f Fx(\\)h(\001)e(\001)g(\001) g(\\)i(D)s FB(\()p Fx(L)1878 3197 y Ft(R)1938 3205 y Fm(n)1984 3234 y FB(\))p Fy(:)31 b FB(When)h(the)f(coupling)g Fy(g)g FB(=)d(0,)j(the)g(pure)324 3354 y(p)s(oin)m(t)e(sp)s(ectrum)h (of)e Fx(L)1173 3369 y Fw(0)1241 3354 y FB(is)h Fy(\033)1390 3369 y Fv(pp)1466 3354 y FB(\()p Fx(L)1573 3369 y Fw(0)1612 3354 y FB(\))e(=)h Fx(f\000)p FB(2)p Fy(!)2018 3369 y Fw(0)2057 3354 y Fy(;)17 b FB(0)p Fy(;)g FB(2)p Fy(!)2304 3369 y Fw(0)2342 3354 y Fx(g)p FB(,)30 b(with)f(double)g(degeneracy)i (at)324 3474 y(0,)h(and)h(the)g(con)m(tin)m(uous)h(sp)s(ectrum)g(of)e Fx(L)1884 3489 y Fw(0)1956 3474 y FB(is)h Fy(\033)2109 3489 y Fv(cont)2247 3474 y FB(\()p Fx(L)2354 3489 y Fw(0)2393 3474 y FB(\))27 b(=)h Fq(R)p FB(.)43 b(It)32 b(follo)m(ws)i(that)728 3699 y Fy(\033)783 3714 y Fv(pp)859 3699 y FB(\()p Fy(K)980 3714 y Fw(0)1019 3699 y FB(\))28 b(=)f Fx(f)p Fy(E)1316 3648 y Fw(\()p Fv(k)r Fw(\))1310 3724 y Fv(j)1414 3699 y FB(\()p Fy(g)k FB(=)c(0\))h(=)f Fy(E)1923 3714 y Fv(j)1982 3699 y FB(+)22 b Fy(k)s(!)31 b FB(:)d Fy(j)33 b FB(=)28 b(0)p Fy(;)17 b Fx(\001)g(\001)g(\001)31 b Fy(;)17 b FB(3)p Fy(;)g(k)30 b Fx(2)e Fq(Z)p Fx(g)p Fy(;)231 b FB(\(65\))324 3910 y(where)34 b Fy(E)678 3925 y Fw(0)p Fv(;)p Fw(1)800 3910 y FB(=)27 b(0)p Fy(;)17 b(E)1068 3925 y Fw(2)1135 3910 y FB(=)28 b Fx(\000)p FB(2)p Fy(!)1426 3925 y Fw(0)1465 3910 y Fy(;)33 b FB(and)f Fy(E)1786 3925 y Fw(3)1854 3910 y FB(=)27 b(2)p Fy(!)2067 3925 y Fw(0)2106 3910 y Fy(;)33 b FB(and)g Fy(\033)2411 3925 y Fv(cont)2548 3910 y FB(\()p Fy(K)2669 3925 y Fw(0)2708 3910 y FB(\))28 b(=)g Fq(R)p Fy(:)k FB(Let)1559 4121 y Fy(K)1649 4080 y Fw(\006)1732 4121 y FB(:=)c Fx(\000)p Fy(i@)2024 4136 y Fv(t)2077 4121 y FB(+)22 b Fx(L)2244 4080 y Fw(\006)2299 4121 y Fy(:)324 4332 y FB(Clearly)-8 b(,)33 b Fy(\033)t FB(\()p Fy(K)868 4296 y Fw(\006)924 4332 y FB(\))27 b(=)h Fy(\033)1148 4347 y Fv(pp)1223 4332 y FB(\()p Fy(K)1344 4347 y Fw(0)1384 4332 y FB(\))p Fy(:)k FB(W)-8 b(e)33 b(ha)m(v)m(e)h(the)f(follo)m(wing)g(t)m(w)m(o)g (easy)h(lemmas.)324 4570 y Fq(Lemma)39 b(4.1)33 b Fu(F)-7 b(or)34 b Fy(\022)c Fx(2)e Fq(C)p Fu(,)35 b(the)g(fol)5 b(lowing)34 b(holds.)p Black 409 4766 a(\(i\))p Black 49 w(F)-7 b(or)34 b(any)g Fy( )e Fx(2)c(D)s Fu(,)35 b(one)f(has)1112 4977 y Fx(k)p Fy(K)1245 4992 y Fw(0)1284 4977 y FB(\()p Fy(\022)s FB(\))p Fy( )t Fx(k)1525 4936 y Fw(2)1592 4977 y FB(=)28 b Fx(k)p Fy(K)1829 4992 y Fw(0)1868 4977 y FB(\()p Fy(R)q(e\022)s FB(\))p Fy( )t Fx(k)2229 4936 y Fw(2)2291 4977 y FB(+)22 b Fx(j)p Fy(I)8 b(m\022)s Fx(j)2629 4936 y Fw(2)2668 4977 y Fx(k)p Fy(N)i( )t Fx(k)2923 4936 y Fw(2)2990 4977 y Fy(:)371 b FB(\(66\))p Black 1894 5251 a(19)p Black eop end %%Page: 20 20 TeXDict begin 20 19 bop Black Black Black 379 548 a Fu(\(ii\))p Black 49 w(If)34 b Fy(I)8 b(m\022)31 b Fx(6)p FB(=)d(0)p Fu(,)34 b(then)h Fy(K)1399 563 y Fw(0)1438 548 y FB(\()p Fy(\022)s FB(\))g Fu(is)g(a)f(normal)g(op)-5 b(er)g(ator)35 b(satisfying)1705 745 y Fy(K)1788 760 y Fw(0)1828 745 y FB(\()p Fy(\022)s FB(\))1952 704 y Ft(\003)2019 745 y FB(=)28 b Fy(K)2206 760 y Fw(0)2245 745 y FB(\()p 2283 664 49 4 v Fy(\022)s FB(\))g Fy(;)964 b FB(\(67\))568 943 y Fu(and)34 b Fx(D)s FB(\()p Fy(K)958 958 y Fw(0)997 943 y FB(\()p Fy(\022)s FB(\)\))28 b(=)f Fx(D)s Fu(.)p Black 350 1140 a(\(iii\))p Black 48 w(The)34 b(sp)-5 b(e)g(ctrum)35 b(of)f Fy(K)1374 1155 y Fw(0)1414 1140 y FB(\()p Fy(\022)s FB(\))h Fu(is)1036 1337 y Fy(\033)1091 1352 y Fv(cont)1228 1337 y FB(\()p Fy(K)1349 1352 y Fw(0)1389 1337 y FB(\()p Fy(\022)s FB(\)\))27 b(=)h Fx(f)p Fy(n\022)d FB(+)d Fy(s)28 b FB(:)g Fy(n)f Fx(2)i Fq(N)p Fx(nf)p FB(0)p Fx(g)d FB(a)p Fy(nd)h(s)h Fx(2)g Fq(R)p Fx(g)p Fy(;)294 b FB(\(68\))1098 1483 y Fy(\033)1153 1498 y Fv(pp)1228 1483 y FB(\()p Fy(K)1349 1498 y Fw(0)1389 1483 y FB(\()p Fy(\022)s FB(\)\))27 b(=)h Fx(f)p Fy(k)s(!)d FB(+)d Fy(E)2042 1498 y Fv(j)2107 1483 y FB(:)27 b Fy(j)34 b FB(=)28 b(0)p Fy(;)17 b Fx(\001)g(\001)g(\001)30 b Fy(;)17 b FB(3)p Fy(;)g(k)30 b Fx(2)e Fq(Z)p Fx(g)p Fy(;)351 b FB(\(69\))568 1680 y Fu(wher)-5 b(e)30 b Fy(E)911 1695 y Fw(0)p Fv(;)p Fw(1)1033 1680 y FB(=)e(0)p Fy(;)17 b(E)1302 1695 y Fw(2)1369 1680 y FB(=)27 b Fx(\000)p FB(2)p Fy(!)1659 1695 y Fw(0)1730 1680 y Fu(and)k Fy(E)1988 1695 y Fw(3)2055 1680 y FB(=)c(2)p Fy(!)2268 1695 y Fw(0)2307 1680 y Fy(;)32 b Fu(\(the)f(eigenvalues)f(of)h Fx(L)3251 1644 y Fw(\006)3306 1680 y Fu(\),)g(and)568 1801 y Fy(!)g FB(=)773 1761 y Fw(2)p Fv(\031)p 773 1778 79 4 v 793 1835 a(\034)861 1801 y Fy(:)324 2103 y Fu(Pr)-5 b(o)g(of.)40 b FB(The)26 b(\014rst)f(claim)g(follo)m(ws)h(directly)g(b)m(y)g(lo)s(oking)e(at)h (the)g(sector)h(where)g Fy(N)38 b FB(=)27 b Fy(n)p Fq(1)p Fy(;)324 2223 y FB(since)34 b Fy(K)646 2238 y Fw(0)685 2223 y FB(\()p Fy(\022)s FB(\))f(restricted)h(to)e(this)h(sector)h(is)f (reduced)h(to)1178 2434 y Fy(K)1268 2383 y Fw(\()p Fv(n)p Fw(\))1261 2459 y(0)1370 2434 y FB(\()p Fy(\022)s FB(\))28 b(=)g Fy(K)1716 2393 y Fw(\006)1793 2434 y FB(+)22 b Fy(s)1937 2449 y Fw(1)1999 2434 y FB(+)g Fx(\001)17 b(\001)g(\001)j FB(+)i Fy(s)2379 2449 y Fv(n)2448 2434 y FB(+)g Fy(n\022)31 b(;)681 b FB(\(70\))324 2632 y(where)28 b Fy(s)646 2647 y Fw(1)685 2632 y Fy(;)17 b Fx(\001)g(\001)g(\001)31 b Fy(;)17 b(s)968 2647 y Fv(n)1041 2632 y FB(are)27 b(in)m(terpreted)h (as)f(one-particle)g(m)m(ultiplication)h(op)s(erators.)41 b(F)-8 b(or)324 2752 y Fy(I)8 b(m\022)31 b Fx(6)p FB(=)c(0)p Fy(;)33 b FB(it)f(also)h(follo)m(ws)g(from)g(\(70\))e(that)496 2967 y Fx(D)f FB(=)e Fx(f)p Fy( )j FB(=)d Fx(f)p Fy( )1072 2926 y Fw(\()p Fv(n)p Fw(\))1173 2967 y Fx(g)g FB(:)g Fy( )1373 2926 y Fw(\()p Fv(n)p Fw(\))1502 2967 y Fx(2)g(D)s FB(\()p Fy(K)1804 2916 y Fw(\()p Fv(n)p Fw(\))1797 2991 y(0)1906 2967 y FB(\()p Fy(\022)s FB(\)\))f(a)p Fy(nd)2297 2872 y Fo(X)2348 3082 y Fv(n)2458 2967 y Fx(k)p Fy(K)2598 2916 y Fw(\()p Fv(n)p Fw(\))2591 2991 y(0)2700 2967 y FB(\()p Fy(\022)s FB(\))p Fy( )2891 2926 y Fw(\()p Fv(n)p Fw(\))2993 2967 y Fx(k)3043 2926 y Fw(2)3110 2967 y Fy(<)g Fx(1g)p Fy(;)324 3252 y FB(and)e(hence)i Fy(K)853 3267 y Fw(0)893 3252 y FB(\()p Fy(\022)s FB(\))e(is)h(a)f(closed)i(normal)e (op)s(erator)g(on)g Fx(D)s FB(.)41 b(Claims)27 b(\(ii\))e(and)h (\(iii\))f(follo)m(w)324 3386 y(from)32 b(the)h(corresp)s(onding)h (statemen)m(ts)g(on)f Fy(K)2066 3335 y Fw(\()p Fv(n)p Fw(\))2059 3410 y(0)2168 3386 y FB(\()p Fy(\022)s FB(\).)43 b Fh(\003)324 3624 y Fq(Lemma)c(4.2)470 3745 y Fu(Supp)-5 b(ose)39 b(\(A1\)-\(A3\))g(hold,)g(and)g(assume)g(that)g FB(\()p Fy(g)t(;)17 b(\022)s FB(\))35 b Fx(2)i Fq(C)25 b Fx(\002)h Fy(I)2928 3708 y Ft(\000)2987 3745 y FB(\()p Fy(\016)t FB(\))p Fy(:)39 b Fu(Then)g(the)324 3865 y(fol)5 b(lowing)33 b(holds.)p Black 409 4067 a(\(i\))p Black 49 w Fx(D)s FB(\()p Fy(K)776 4031 y Ft(\003)769 4092 y Fv(g)815 4067 y FB(\()p Fy(\022)s FB(\)\))27 b(=)h Fx(D)37 b Fu(and)e FB(\()p Fy(K)1540 4031 y Ft(\003)1533 4092 y Fv(g)1579 4067 y FB(\()p Fy(\022)s FB(\)\))1741 4031 y Ft(\003)1808 4067 y FB(=)28 b Fy(K)p 1995 4045 41 3 v 15 x Fv(g)2035 4067 y FB(\()p 2073 3986 49 4 v Fy(\022)s FB(\))p Fu(.)p Black 379 4264 a(\(ii\))p Black 49 w(The)34 b(map)g FB(\()p Fy(g)t(;)17 b(\022)s FB(\))27 b Fx(!)g Fy(K)1444 4228 y Ft(\003)1437 4289 y Fv(g)1484 4264 y FB(\()p Fy(\022)s FB(\))35 b Fu(fr)-5 b(om)34 b Fq(C)22 b Fx(\002)h Fy(I)2127 4228 y Ft(\000)2186 4264 y FB(\()p Fy(\016)t FB(\))35 b Fu(to)g(the)g(set)g(of)f(close)-5 b(d)34 b(op)-5 b(er)g(ators)568 4402 y(on)734 4376 y FB(~)705 4402 y Fx(H)34 b Fu(is)e(an)g(analytic)h(family)f(\(of)g(typ) -5 b(e)33 b(A\))g(in)g(e)-5 b(ach)32 b(variable)f(sep)-5 b(ar)g(ately;)33 b(\(se)-5 b(e)568 4522 y([Ka1],)34 b(chapter)g(V,)h (se)-5 b(ction)35 b(3.2\).)p Black 350 4719 a(\(iii\))p Black 48 w(F)-7 b(or)34 b Fy(g)d Fx(2)d Fq(R)34 b Fu(and)g Fy(I)8 b(mz)40 b Fu(lar)-5 b(ge)35 b(enough,)1130 4916 y Fy(s)23 b Fx(\000)56 b FB(lim)1298 4979 y Fv(I)5 b(m\022)r Ft(")p Fw(0)1502 4916 y FB(\()p Fy(K)1630 4875 y Ft(\003)1623 4941 y Fv(g)1669 4916 y FB(\()p Fy(\022)s FB(\))23 b Fx(\000)f Fy(z)t FB(\))2002 4875 y Ft(\000)p Fw(1)2125 4916 y FB(=)27 b(\()p Fy(K)2356 4875 y Ft(\003)2349 4941 y Fv(g)2396 4916 y FB(\()p Fy(R)q(e\022)s FB(\))22 b Fx(\000)h Fy(z)t FB(\))2849 4875 y Ft(\000)p Fw(1)2972 4916 y Fy(:)389 b FB(\(71\))p Black 1894 5251 a(20)p Black eop end %%Page: 21 21 TeXDict begin 21 20 bop Black Black 324 548 a Fu(Pr)-5 b(o)g(of.)64 b FB(The)41 b(\014rst)f(claim)h(\(i\))e(follo)m(ws)i(from) e(the)i(fact)e(that)h Fy(g)2695 523 y FB(~)2681 548 y Fy(V)2759 512 y Fv(tot)2848 548 y FB(\()p Fy(t;)17 b(\022)s FB(\))40 b(is)g(b)s(ounded)324 668 y(for)f Fy(\022)44 b Fx(2)d Fy(I)8 b FB(\()p Fy(\016)t FB(\).)65 b(It)40 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y(~)1063 3245 y Fy(T)1120 3261 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))1301 3245 y FB(:=)1453 3220 y(~)1432 3245 y Fy(P)1495 3261 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))1669 3220 y FB(~)1647 3245 y Fy(P)1710 3261 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))1863 3245 y FB(\()p Fy(\022)s FB(\))2009 3220 y(~)1987 3245 y Fy(P)2050 3261 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))2202 3245 y Fy(:)2229 3209 y Fw(7)2299 3245 y FB(W)-8 b(e)32 b(sho)m(w)f(in)g(Theorem)h(4.3)f(that)324 3366 y(the)i(isomorphism)469 3548 y(~)452 3573 y Fy(S)512 3589 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))665 3573 y FB(\()p Fy(\022)s FB(\))28 b(:=)967 3548 y(~)947 3573 y Fy(T)1018 3522 y Ft(\000)p Fw(1)p Fv(=)p Fw(2)1004 3605 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))1205 3548 y FB(~)1183 3573 y Fy(P)1246 3589 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))1420 3548 y FB(~)1398 3573 y Fy(P)1461 3589 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))1614 3573 y FB(\()p Fy(\022)s FB(\))g(:)g Fy(R)q(an)p FB(\()2065 3548 y(~)2043 3573 y Fy(P)2106 3589 y Fv(g)r(;)p Fw(\()p Fv(k)r 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Fj(k)q Fs(\))2490 4902 y Fr(is)h(w)n(ell-de\014ned)f(b)n(y)g(the)g(sp)r(ectral)324 5002 y(theorem.)p Black Black 1894 5251 a FB(21)p Black eop end %%Page: 22 22 TeXDict begin 22 21 bop Black Black 470 548 a FB(Let)30 b Fy(k)g FB(=)e Fy(min)p Fx(f)p Fy(\016)n(;)1164 509 y Fv(\031)p 1149 525 75 4 v 1149 582 a(\014)1189 591 y Fn(1)1233 548 y Fy(;)17 b Fx(\001)g(\001)g(\001)31 b Fy(;)1499 509 y Fv(\031)p 1480 525 83 4 v 1480 582 a(\014)1520 590 y Fm(n)1572 548 y Fx(g)p Fy(;)e FB(where)i Fy(\016)i FB(app)s(ears)c(in)h(assumption)h(\(A2\),)e(section)324 668 y(3,)g(and)h Fy(\014)671 683 y Fw(1)710 668 y Fy(;)17 b Fx(\001)g(\001)g(\001)31 b Fy(;)17 b(\014)1002 683 y Fv(n)1049 668 y Fy(;)29 b FB(are)g(the)h(in)m(v)m(erse)h(temp)s (eratures)g(of)e(the)g(reserv)m(oirs)i Fx(R)3126 683 y Fw(1)3166 668 y Fy(;)17 b Fx(\001)g(\001)g(\001)31 b Fy(;)17 b Fx(R)3487 683 y Fv(n)3535 668 y Fy(;)324 789 y FB(resp)s(ectiv)m(ely)-8 b(.)46 b(F)-8 b(or)32 b Fy(\022)f Fx(2)d Fy(I)1281 753 y Ft(\000)1340 789 y 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Fu(Supp)-5 b(ose)42 b(that)h(assumptions)e(\(A1\)-\(A3\))i(hold.)66 b(Then,)44 b(for)e Fy(g)2873 2243 y Fw(1)2954 2228 y Fy(>)g FB(0)g Fu(satisfying)324 2349 y(\(79\),)34 b Fy(\022)d Fx(2)d Fy(I)789 2313 y Ft(\000)848 2349 y FB(\()p Fy(k)s FB(\))35 b Fu(and)f Fy(\027)41 b Fu(satisfying)35 b(\(78\),)f(the)h(fol)5 b(lowing)33 b(holds.)p Black 409 2545 a(\(i\))p Black 49 w(If)40 b Fx(j)p Fy(g)t Fx(j)d Fy(<)i(g)982 2560 y Fw(1)1021 2545 y Fu(,)j(the)f(essential)e(sp)-5 b(e)g(ctrum)41 b(of)g(the)f(op)-5 b(er)g(ator)41 b Fy(K)2846 2509 y Ft(\003)2839 2570 y Fv(g)2885 2545 y FB(\()p Fy(\022)s FB(\))g Fu(is)g(c)-5 b(ontaine)g(d)568 2666 y(in)40 b(the)h(half-plane) e Fq(C)p Fx(n)p FB(\004\()p Fy(\027)6 b FB(\))p Fy(;)41 b Fu(wher)-5 b(e)41 b FB(\004\()p Fy(\027)6 b FB(\))39 b(:=)f Fx(f)p Fy(z)44 b Fx(2)39 b Fq(C)g FB(:)g Fy(I)8 b(mz)43 b Fx(\025)c Fy(\027)6 b Fx(g)p Fy(:)42 b Fu(Mor)-5 b(e-)568 2786 y(over,)42 b(the)g(discr)-5 b(ete)41 b(sp)-5 b(e)g(ctrum)41 b(of)g Fy(K)1981 2750 y Ft(\003)1974 2811 y Fv(g)2021 2786 y FB(\()p Fy(\022)s FB(\))g Fu(is)g(indep)-5 b(endent)40 b(of)i Fy(\022)h Fx(2)d Fy(I)3211 2750 y Ft(\000)3270 2786 y FB(\()p Fy(k)s FB(\))p Fu(.)64 b(If)568 2923 y Fx(j)p Fy(g)t Fx(j)26 b Fy(<)814 2884 y Fw(1)p 814 2900 36 4 v 814 2958 a(2)860 2923 y Fy(g)907 2938 y Fw(1)946 2923 y Fu(,)j(then)e(the)h(sp)-5 b(e)g(ctr)g(al)27 b(pr)-5 b(oje)g(ctions)2216 2898 y FB(~)2194 2923 y Fy(P)2257 2939 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))2410 2923 y FB(\()p Fy(\022)s FB(\))p Fy(;)17 b(k)30 b Fx(2)e Fq(Z)p Fy(;)g Fu(asso)-5 b(ciate)g(d)27 b(to)h(the)568 3044 y(sp)-5 b(e)g(ctrum)34 b(of)g Fy(K)1181 3007 y Ft(\003)1174 3068 y Fv(g)1221 3044 y FB(\()p Fy(\022)s FB(\))h Fu(in)f(the)h(half-plane)e FB(\004\()p Fy(\027)6 b FB(\))p Fy(;)35 b Fu(ar)-5 b(e)34 b(analytic)g(in)h Fy(g)j Fu(and)c(satisfy)568 3164 y(the)h(estimate) 1559 3284 y Fx(k)1631 3259 y FB(~)1609 3284 y Fy(P)1672 3300 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))1825 3284 y FB(\()p Fy(\022)s FB(\))22 b Fx(\000)2092 3259 y FB(~)2071 3284 y Fy(P)2134 3300 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))2286 3284 y Fx(k)27 b Fy(<)h FB(1)f Fy(:)818 b FB(\(81\))p Black 379 3496 a Fu(\(ii\))p Black 49 w(If)45 b Fx(j)p Fy(g)t Fx(j)h Fy(<)968 3452 y Fv(g)1002 3461 y Fn(1)p 968 3473 69 4 v 984 3530 a Fw(2)1046 3496 y Fu(,)j(then)c(the)h (quasi-Flo)-5 b(quet)45 b(Liouvil)5 b(le)-5 b(an)2654 3470 y FB(~)2643 3496 y(\006)2713 3511 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))2912 3496 y Fu(de\014ne)g(d)45 b(in)g(\(77\))568 3616 y(dep)-5 b(ends)33 b(analytic)-5 b(al)5 b(ly)35 b(on)f Fy(g)t Fu(,)g(and)h(has)f(a)h(T)-7 b(aylor)34 b(exp)-5 b(ansion)1494 3853 y FB(~)1483 3879 y(\006)1553 3894 y Fv(g)r(;)p Fw(\()p Fv(k)r Fw(\))1734 3879 y FB(=)28 b Fy(K)1928 3837 y Fw(\006)1921 3903 y(\()p Fv(k)r Fw(\))2041 3879 y FB(+)2175 3754 y Ft(1)2139 3784 y Fo(X)2149 3994 y Fv(j)t Fw(=1)2299 3879 y Fy(g)2350 3837 y Fw(2)p Fv(j)2432 3853 y FB(~)2421 3879 y(\006)2491 3828 y Fw(\(2)p Fv(j)t Fw(\))2491 3910 y(\()p Fv(k)r Fw(\))3388 3879 y FB(\(82\))568 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Fw(\()p Fv(j)t Fw(\))2357 2561 y(\()p Fv(k)r Fw(\))2487 2530 y Fy(;)874 b FB(\(89\))324 2794 y(with)360 3003 y(~)324 3028 y Fy(M)428 2977 y Fw(\()p Fv(j)t Fw(\))418 3059 y(\()p Fv(k)r Fw(\))548 3028 y FB(=)651 2892 y Fo(I)707 3118 y Fv(\015)798 2960 y Fy(dz)p 778 3005 V 778 3096 a FB(2)p Fy(\031)t(i)928 3028 y(z)t FB(\()p Fy(z)t Fx(\000)p Fy(K)1231 2987 y Fw(\006)1289 3028 y FB(\))1327 2987 y Ft(\000)p Fw(1)1443 3003 y FB(~)1421 3028 y Fy(P)1484 3043 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))1651 3003 y FB(~)1636 3028 y Fy(V)1715 2987 y Fv(tot)1804 3028 y FB(\()p Fx(\001)p Fy(;)17 b(\022)s FB(\)\(\()p Fy(z)t Fx(\000)p Fy(K)2292 2987 y Ft(\003)2285 3052 y Fw(0)2332 3028 y FB(\()p Fy(\022)s FB(\)\))2494 2987 y Ft(\000)p Fw(1)2603 3003 y FB(~)2588 3028 y Fy(V)2667 2987 y Fv(tot)2756 3028 y FB(\()p Fx(\001)p Fy(;)g(\022)s FB(\)\))2990 2987 y Fv(j)t Ft(\000)p Fw(1)3138 3003 y FB(~)3116 3028 y Fy(P)3179 3043 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))3332 3028 y FB(\()p Fy(z)t Fx(\000)p Fy(K)3586 2987 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617 y Fw(\()p Fv(k)r Fw(\))396 694 y Fv(j)499 668 y FB(\()p Fy(g)31 b FB(=)d(0\))p Fy(;)17 b(j)33 b FB(=)27 b(0)p Fy(;)17 b Fx(\001)g(\001)g(\001)31 b Fy(;)17 b FB(3)p Fy(;)g(k)30 b Fx(2)e Fq(Z)p Fy(;)33 b FB(are)1114 896 y Fy(\036)1172 855 y Fw(0)1172 920 y Fv(k)1242 896 y FB(=)27 b Fy(e)1390 855 y Fv(ik)r(!)1526 896 y Fx(\012)22 b Fy(e)1670 911 y Fw(1)1732 896 y Fx(\012)h Fy(e)1877 911 y Fw(1)1938 896 y Fx(\012)2049 871 y FB(~)2038 896 y(\012)2108 855 y Ft(R)2168 864 y Fn(1)2230 896 y Fx(\012)f(\001)17 b(\001)g(\001)k(\012)2578 871 y FB(~)2567 896 y(\012)2637 855 y Ft(R)2697 863 y Fm(n)2745 896 y Fy(;)1114 1056 y(\036)1172 1015 y Fw(1)1172 1081 y Fv(k)1242 1056 y FB(=)27 b Fy(e)1390 1015 y Fv(ik)r(!)1526 1056 y Fx(\012)22 b Fy(e)1670 1071 y Fw(2)1732 1056 y Fx(\012)h Fy(e)1877 1071 y Fw(2)1938 1056 y Fx(\012)2049 1031 y FB(~)2038 1056 y(\012)2108 1015 y Ft(R)2168 1024 y Fn(1)2230 1056 y Fx(\012)f(\001)17 b(\001)g(\001)k(\012)2578 1031 y FB(~)2567 1056 y(\012)2637 1015 y Ft(R)2697 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Ft(R)1921 1707 y Fm(i)1951 1733 y FB(\()p Fy(L)2055 1697 y Fw(2)2095 1733 y FB(\()p Fq(R)p FB(;)17 b Fx(B)s FB(\)\))p Fy(:)470 1867 y FB(W)-8 b(e)33 b(apply)g(p)s(erturbation)g (theory)g(to)g(calculate)g Fy(E)2388 1816 y Fw(\()p Fv(k)r Fw(\))2382 1892 y Fv(j)2486 1867 y FB(\()p Fy(g)t FB(\))p Fy(:)e FB(W)-8 b(e)33 b(kno)m(w)h(that)392 2114 y(~)381 2140 y(\006)451 2089 y Fw(\(2\))451 2171 y(\()p Fv(k)r Fw(\))632 2140 y FB(=)801 2072 y(1)p 801 2117 49 4 v 801 2208 a(2)876 2004 y Fo(I)931 2229 y Fv(\015)967 2241 y Fm(k)1057 2072 y Fy(dz)p 1036 2117 141 4 v 1036 2208 a FB(2)p Fy(\031)t(i)1187 2140 y Fx(f)1259 2114 y FB(~)1237 2140 y Fy(P)1300 2155 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))1467 2114 y FB(~)1453 2140 y Fy(V)1531 2098 y Fv(tot)1620 2140 y FB(\()p Fx(\001)p Fy(;)17 b(\022)s FB(\)\()p Fy(z)27 b Fx(\000)22 b Fy(K)2108 2155 y Fw(0)2148 2140 y FB(\()p Fy(\022)s FB(\)\))2310 2098 y Ft(\000)p Fw(1)2419 2114 y FB(~)2404 2140 y Fy(V)2482 2098 y Fv(tot)2572 2140 y FB(\()p Fx(\001)p Fy(;)17 b(\022)s FB(\))2789 2114 y(~)2768 2140 y Fy(P)2831 2155 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))2982 2140 y FB(\()p Fy(z)27 b Fx(\000)c Fy(K)3282 2098 y Fw(\006)3275 2164 y(\()p Fv(k)r Fw(\))3372 2140 y FB(\))3410 2098 y Ft(\000)p Fw(1)632 2367 y FB(+)83 b(\()p Fy(z)26 b Fx(\000)d Fy(K)1090 2326 y Fw(\006)1083 2392 y(\()p Fv(k)r Fw(\))1181 2367 y FB(\))1241 2342 y(~)1219 2367 y Fy(P)1282 2382 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))1449 2342 y FB(~)1434 2367 y Fy(V)1512 2326 y Fv(tot)1602 2367 y FB(\()p Fx(\001)p Fy(;)17 b(\022)s FB(\)\()p Fy(z)26 b Fx(\000)d Fy(K)2090 2382 y Fw(0)2129 2367 y FB(\()p Fy(\022)s FB(\)\))2291 2326 y Ft(\000)p Fw(1)2400 2342 y FB(~)2385 2367 y Fy(V)2464 2326 y Fv(tot)2553 2367 y FB(\()p Fx(\001)p Fy(;)17 b(\022)s FB(\))2770 2342 y(~)2749 2367 y Fy(P)2812 2382 y Fw(0)p Fv(;)p Fw(\()p Fv(k)r Fw(\))2964 2367 y Fx(g)27 b Fy(:)p Black 320 w FB(\(93\))p Black 324 2577 a(F)-8 b(or)32 b Fy(f)547 2592 y Fv(\014)s(;\026)688 2577 y FB(as)h(in)g(\(27\),)f(w)m(e)i(let)e (its)i(F)-8 b(ourier)32 b(transform)h(b)s(e)1149 2814 y(^)1128 2840 y Fy(f)1176 2855 y Fv(\014)s(;\026;m)1367 2840 y FB(\()p Fy(u;)17 b(!)t FB(\))26 b(:=)1777 2773 y(1)p 1775 2817 54 4 v 1775 2909 a Fy(\034)1855 2705 y Fo(Z)1955 2731 y Fv(\034)1910 2930 y Fw(0)2014 2840 y Fy(dte)2145 2799 y Ft(\000)p Fv(im!)r(t)2363 2840 y Fy(f)2411 2855 y Fv(\014)s(;\026)2520 2840 y FB(\()p Fy(u;)17 b(t)p FB(\))p Fy(:)630 b FB(\(94\))324 3121 y(Similarly)-8 b(,)33 b(for)f Fy(f)965 3074 y Fw(#)954 3149 y Fv(\014)s(;\026)1096 3121 y FB(as)h(in)g(\(28\),)f(w)m(e)h(let) 1149 3371 y(^)1128 3398 y Fy(f)1187 3350 y Fw(#)1176 3425 y Fv(\014)s(;\026;m)1367 3398 y FB(\()p Fy(u;)17 b(!)t FB(\))26 b(:=)1777 3330 y(1)p 1775 3375 V 1775 3466 a Fy(\034)1855 3262 y Fo(Z)1955 3288 y Fv(\034)1910 3488 y Fw(0)2014 3398 y Fy(dte)2145 3356 y Ft(\000)p Fv(im!)r(t)2363 3398 y Fy(f)2422 3350 y Fw(#)2411 3425 y Fv(\014)s(;\026)2520 3398 y FB(\()p Fy(u;)17 b(t)p FB(\))p Fy(:)630 b FB(\(95\))470 3686 y(Consider)42 b(\014rst)f(the)f (nondegenerate)i(eigen)m(v)-5 b(alue)42 b Fy(E)2474 3635 y Fw(\()p Fv(k)r Fw(\))2468 3710 y(3)2571 3686 y Fy(:)f FB(Applying)g(the)g(Cauc)m(h)m(y)324 3806 y(in)m(tegration)33 b(form)m(ula)f(to)h(\(93\),)f(and)g(using)i(the)f(facts)f(that)877 4061 y(lim)877 4123 y Fv(\017)p Ft(&)p Fw(0)1029 4061 y Fy(R)q(e)1260 3993 y FB(1)p 1159 4038 250 4 v 1159 4129 a Fy(x)23 b Fx(\000)f Fy(i\017)1447 4061 y FB(=)27 b Fx(P)8 b Fy(V)1720 3993 y FB(1)p 1716 4038 56 4 v 1716 4129 a Fy(x)1782 4061 y(;)44 b FB(a)p Fy(nd)g FB(lim)2056 4123 y Fv(\017)p Ft(&)p Fw(0)2207 4061 y Fy(I)8 b(m)2454 3993 y FB(1)p 2353 4038 250 4 v 2353 4129 a Fy(x)23 b Fx(\000)f Fy(i\017)2641 4061 y FB(=)27 b Fy(\031)t(\016)t FB(\()p Fy(x)p FB(\))p Fy(;)324 4313 y FB(where)34 b Fx(P)8 b Fy(V)54 b FB(denotes)34 b(the)f(Cauc)m(h)m(y)i(principal)e(v) -5 b(alue,)33 b(it)g(follo)m(ws)g(that)484 4593 y Fy(R)q(e)28 b Fx(\034)g Fy(\036)818 4552 y Fw(3)818 4618 y Fv(k)860 4593 y Fy(;)915 4568 y FB(~)904 4593 y(\006)974 4542 y Fv(k)r Fw(\(2\))974 4618 y(3)1107 4593 y Fy(\036)1165 4552 y Fw(3)1165 4618 y Fv(k)1235 4593 y Fx(\035)83 b FB(=)1584 4499 y Fo(X)1577 4710 y Fv(m)p Ft(2)p Fp(Z)1803 4469 y Fv(n)1752 4499 y Fo(X)1767 4709 y Fv(i)p Fw(=1)1913 4593 y Fx(P)8 b Fy(V)2086 4458 y Fo(Z)2141 4683 y Fp(R)2222 4593 y Fy(du)2423 4526 y Fx(k)2494 4500 y FB(^)2473 4526 y Fy(f)2521 4541 y Fv(\014)2561 4551 y Fm(i)2587 4541 y Fv(;\026)2649 4551 y Fm(i)2676 4541 y Fv(;m)2762 4526 y FB(\()p Fy(u;)17 b(!)t FB(\))p Fx(k)3053 4490 y Fw(2)3053 4551 y Ft(B)p 2339 4570 850 4 v 2339 4662 a FB(2)p Fy(!)2449 4677 y Fw(0)2510 4662 y Fx(\000)22 b FB(\()p Fy(k)j Fx(\000)e Fy(m)p FB(\))p Fy(!)j Fx(\000)c Fy(u)3226 4593 y(;)468 4921 y(I)8 b(m)28 b Fx(\034)g Fy(\036)818 4880 y Fw(3)818 4945 y Fv(k)860 4921 y Fy(;)915 4896 y FB(~)904 4921 y(\006)974 4870 y Fv(k)r Fw(\(2\))974 4945 y(3)1107 4921 y Fy(\036)1165 4880 y Fw(3)1165 4945 y Fv(k)1235 4921 y Fx(\035)83 b FB(=)g Fx(\000)p Fy(\031)1737 4826 y Fo(X)1730 5038 y Fv(m)p Ft(2)p Fp(Z)1956 4796 y Fv(n)1905 4826 y Fo(X)1920 5036 y Fv(i)p Fw(=1)2066 4921 y Fx(k)2137 4894 y FB(^)2116 4921 y Fy(f)2164 4936 y Fv(\014)2204 4946 y Fm(i)2230 4936 y Fv(;\026)2292 4946 y Fm(i)2318 4936 y Fv(;m)2404 4921 y FB(\(2)p Fy(!)2552 4936 y Fw(0)2613 4921 y Fx(\000)23 b FB(\()p Fy(k)i Fx(\000)e Fy(m)p FB(\))p Fy(!)t(;)17 b(!)t FB(\))p Fx(k)3312 4880 y Fw(2)3312 4945 y Ft(B)3390 4921 y Fy(;)p Black 1894 5251 a FB(25)p Black eop end %%Page: 26 26 TeXDict begin 26 25 bop Black Black 324 548 a FB(where)34 b Fx(\034)27 b(\001)p Fy(;)17 b Fx(\001)27 b(\035)32 b FB(is)h(the)g(scalar)g(pro)s(duct)g(on)2065 523 y(~)2036 548 y Fx(H)q Fy(:)g FB(Therefore,)570 825 y Fy(E)648 774 y Fw(\()p Fv(k)r Fw(\))642 849 y(3)745 825 y FB(\()p Fy(g)t FB(\))27 b(=)h Fy(k)s(!)d FB(+)d(2)p Fy(!)1351 840 y Fw(0)1412 825 y FB(+)g Fy(g)1561 784 y Fw(2)1624 730 y Fo(X)1617 942 y Fv(m)p Ft(2)p Fp(Z)1843 700 y Fv(n)1793 730 y Fo(X)1807 940 y Fv(i)p Fw(=1)1953 825 y Fx(P)8 b Fy(V)2126 689 y Fo(Z)2181 915 y 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-1 scale % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index oldshow % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proc char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % this is the pattern fill program from the Second edition Reference Manual % with changes to call the above pattern fill % left30 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 16 true [ 32 0 0 -16 0 16 ] {} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P1 exch def /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0 slj 0 slc 0.05669 0.05669 sc % % Fig objects follow % % % here starts figure with depth 50 % Ellipse 7.500 slw n 9090 2475 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col7 s gr % Ellipse n 8640 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 9540 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 9090 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7920 2475 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col7 s gr % Ellipse n 7470 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 8370 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7920 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6750 2475 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col7 s gr % Ellipse n 6300 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7200 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6750 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 5580 2475 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col7 s gr % Ellipse n 5130 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6030 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 5580 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4455 2475 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col7 s gr % Ellipse n 4005 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4905 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4455 2790 45 45 0 360 DrawEllipse gs col0 s gr % Polyline 0 slj 0 slc n 3780 2475 m 9855 2475 l gs col0 s gr % Polyline n 3780 3420 m 9810 3420 l 9810 4770 l 3780 4770 l cp gs /PC [[0.00 1.00 1.00] [0.00 1.00 1.00]] def 15.00 15.00 sc P1 [16 0 0 -8 252.00 228.00] PATmp PATsp ef gr PATusp gs col3 s gr % Polyline gs clippath 4965 3628 m 4965 3795 l 5025 3795 l 5025 3628 l 5025 3628 l 4995 3748 l 4965 3628 l cp 5025 2627 m 5025 2460 l 4965 2460 l 4965 2627 l 4965 2627 l 4995 2507 l 5025 2627 l cp eoclip n 4995 2475 m 4995 3780 l gs col0 s gr gr % arrowhead n 5025 2627 m 4995 2507 l 4965 2627 l 5025 2627 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 4965 3628 m 4995 3748 l 5025 3628 l 4965 3628 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 4605 3853 m 4605 4020 l 4665 4020 l 4665 3853 l 4665 3853 l 4635 3973 l 4605 3853 l cp 4665 2627 m 4665 2460 l 4605 2460 l 4605 2627 l 4605 2627 l 4635 2507 l 4665 2627 l cp eoclip n 4635 2475 m 4635 4005 l gs col0 s gr gr % arrowhead n 4665 2627 m 4635 2507 l 4605 2627 l 4665 2627 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 4605 3853 m 4635 3973 l 4665 3853 l 4605 3853 l cp gs 0.00 setgray ef gr col0 s % Polyline [60] 0 sd n 3735 4005 m 9810 4005 l gs col0 s gr [] 0 sd /Times-Roman ff 190.50 scf sf 6975 3330 m gs 1 -1 sc ( ) col0 sh gr /Times-Roman ff 190.50 scf sf 6705 2340 m gs 1 -1 sc (0) col0 sh gr % here ends figure; $F2psEnd rs end showpage %%Trailer %EOF %%EndDocument @endspecial 0 0 0 TeXcolorrgb 795 2652 a Fc(k)p Black 0 0 0 TeXcolorrgb 2984 2206 a FD(2)p Fc(!)p Black 0 0 0 TeXcolorrgb -1781 w FD(-)p 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Fw(2)2042 2172 y Fy(a)2093 2187 y Fw(0)p Fv(;)p Fw(1)2209 2172 y FB(+)g Fy(O)s FB(\()p Fy(g)2474 2131 y Fw(4)2512 2172 y FB(\))28 b Fy(;)734 b FB(\(124\))324 2330 y(where)34 b Fy(a)657 2345 y Fw(0)p Fv(;)p Fw(1)784 2330 y FB(are)e(the)h(eigen)m (v)-5 b(alues)35 b(of)d(the)h(2)22 b Fx(\002)g FB(2)33 b(matrix)324 2606 y Fx(\000)p Fy(i\031)518 2511 y Fo(X)510 2723 y Fv(m)p Ft(2)p Fp(Z)740 2481 y Fw(2)686 2511 y Fo(X)701 2721 y Fv(i)p Fw(=1)846 2606 y Fx(k)917 2580 y FB(^)896 2606 y Fy(f)944 2621 y Fv(\014)984 2631 y Fm(i)1010 2621 y Fv(;\026)1072 2631 y Fm(i)1099 2621 y Fv(;m)1185 2606 y FB(\(2)p Fy(!)1333 2621 y Fw(0)1372 2606 y Fx(\000)p FB(\()p Fy(k)s Fx(\000)p Fy(m)p FB(\))p Fy(!)t(;)17 b(!)t FB(\))p Fx(k)2003 2565 y Fw(2)2003 2630 y Ft(B)2071 2465 y Fo(\022)2540 2545 y FB(1)479 b Fx(\000)p Fy(e)3190 2509 y Ft(\000)p Fv(\014)3285 2519 y Fm(i)3312 2509 y Fw(\(2)p Fv(!)3418 2518 y Fn(0)3453 2509 y Ft(\000)p Fw(\()p Fv(k)r Ft(\000)p Fv(m)p Fw(\))p Fv(!)r Ft(\000)p Fv(\026)p Fw(\))p Fv(=)p Fw(2)2144 2667 y Fx(\000)p Fy(e)2266 2631 y Fv(\014)2306 2641 y Fm(i)2333 2631 y Fw(\(2)p Fv(!)2439 2640 y Fn(0)2474 2631 y Ft(\000)p Fw(\()p Fv(k)r Ft(\000)p Fv(m)p Fw(\))p Fv(!)r Ft(\000)p Fv(\026)p Fw(\))p Fv(=)p Fw(2)3492 2667 y FB(1)3964 2465 y Fo(\023)4082 2606 y Fy(:)3339 2820 y FB(\(125\))324 2940 y(Note)32 b(that,)h(to)f(second)i(order)e(in)h(the)g(coupling)g Fy(g)t(;)f FB(the)h(discrete)h(sp)s(ectrum)g(is)f(b)s(elo)m(w)324 3061 y(the)g(real)f(axis.)45 b(The)33 b(claim)g(of)g(the)g(theorem)g (follo)m(ws)g(b)m(y)h(noting)e(that)1042 3243 y Fy(s)23 b Fx(\000)56 b FB(lim)1210 3306 y Fv(I)5 b(m\022)r Ft(")p Fw(0)1414 3243 y FB(\()1478 3218 y(~)1452 3243 y Fy(K)1535 3258 y Fv(g)1575 3243 y FB(\()p Fy(\022)s FB(\))22 b Fx(\000)h Fy(z)t FB(\))1908 3202 y Ft(\000)p Fw(1)2030 3243 y FB(=)28 b(\()2198 3218 y(~)2172 3243 y Fy(K)2255 3258 y Fv(g)2295 3243 y FB(\()p Fy(R)q(e\022)s FB(\))22 b Fx(\000)h Fy(z)t FB(\))2748 3202 y Ft(\000)p Fw(1)324 3468 y FB(for)32 b(large)g(enough)h Fy(I)8 b(mz)t(:)34 b Fh(\003)p Black Black 502 5002 a @beginspecial 0 @llx 0 @lly 346 @urx 173 @ury 3460 @rwi @setspecial %%BeginDocument: spectrum2.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: spectrum2.fig %%Creator: fig2dev Version 3.2 Patchlevel 5-alpha5 %%CreationDate: Wed Dec 7 19:44:10 2005 %%For: walid@tefnut (Walid Abou Salem) %%BoundingBox: 0 0 346 173 %Magnification: 0.9000 %%EndComments /MyAppDict 100 dict dup begin def /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 173 moveto 0 0 lineto 346 0 lineto 346 173 lineto closepath clip newpath -213.6 295.3 translate 1 -1 scale % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index oldshow % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proc char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % this is the pattern fill program from the Second edition Reference Manual % with changes to call the above pattern fill % left30 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 16 true [ 32 0 0 -16 0 16 ] {} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P1 exch def /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0 slj 0 slc 0.05669 0.05669 sc % % Fig objects follow % % % here starts figure with depth 50 % Ellipse 7.500 slw n 8640 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 9540 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 9090 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7470 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 8370 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7920 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6300 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7200 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6750 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 5130 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6030 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 5580 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4005 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4905 2700 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4455 2790 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 4455 2610 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 5580 2610 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 6750 2610 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 7920 2610 45 45 0 360 DrawEllipse gs col0 s gr % Ellipse n 9090 2610 45 45 0 360 DrawEllipse gs col0 s gr % Polyline 0 slj 0 slc n 3780 2475 m 9855 2475 l gs col0 s gr % Polyline n 3780 3420 m 9810 3420 l 9810 4770 l 3780 4770 l cp gs /PC [[0.00 1.00 1.00] [0.00 1.00 1.00]] def 15.00 15.00 sc P1 [16 0 0 -8 252.00 228.00] PATmp PATsp ef gr PATusp gs col3 s gr % Polyline gs clippath 4605 3853 m 4605 4020 l 4665 4020 l 4665 3853 l 4665 3853 l 4635 3973 l 4605 3853 l cp 4665 2627 m 4665 2460 l 4605 2460 l 4605 2627 l 4605 2627 l 4635 2507 l 4665 2627 l cp eoclip n 4635 2475 m 4635 4005 l gs col0 s gr gr % arrowhead n 4665 2627 m 4635 2507 l 4605 2627 l 4665 2627 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 4605 3853 m 4635 3973 l 4665 3853 l 4605 3853 l cp gs 0.00 setgray ef 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1803 317 4 v 1643 1823 a Fo(p)p 1742 1823 217 4 v 1742 1908 a Fy(m)p FB(\()p Fy(u)p FB(\))1969 1826 y Fy(h)p FB(\()p Fy(u;)17 b(\033)t FB(\))p Fy(;)g(u)26 b(>)i FB(0)f Fy(;)1190 2122 y(g)t FB(\()p Fy(u;)17 b(\033)t FB(\))26 b(:=)1740 2054 y Fy(e)1785 2018 y Ft(\000)p Fv(i )p 1643 2099 372 4 v 1643 2119 a Fo(p)p 1742 2119 273 4 v 1742 2204 a Fy(m)p FB(\()p Fx(j)p Fy(u)p Fx(j)p FB(\))2024 2122 y Fy(h)p FB(\()p Fx(j)p Fy(u)p Fx(j)p Fy(;)17 b(\033)t FB(\))p Fy(;)g(u)26 b(<)h FB(0)h Fy(:)324 2491 y FC(References)p Black 324 2710 a FB([Ar])p Black 225 w(Araki,)i(H.)f(:)42 b(Relativ)m(e)30 b(Hamiltonian)f(for)f(faithful)h(normal)g(states)h(of) e(a)h(v)m(on)714 2831 y(Neumann)38 b(algebra,)h(Publ.)f(Res.)g(Inst.)g (Math.)g(Sci.)g(Ky)m(oto)g(Univ.)g(9,)g(165)714 2951 y(\(1973\))p Black 324 3152 a([ArWy])p Black 74 w(Araki,)32 b(H.)f(and)g(Wyss,)i(W.:)43 b(Represen)m(tations)33 b(of)d(canonical)i (an)m(ticomm)m(u-)714 3273 y(tation)g(relations,)h(Helv.)h(Ph)m(ys.)h (Acta)d Fq(37)p FB(,)h(136)f(\(1964\))p Black 324 3474 a([A-S])p Black 176 w(Ab)s(ou)37 b(Salem,)j(W.:)53 b(On)38 b(the)f(quasi-static)i(ev)m(olution)f(of)f(nonequilibrium)714 3595 y(steady)d(states,)f(mp-arc)g(2005)e(preprin)m(t,)j(submitted)p Black 324 3796 a([A-SF1])p Black 63 w(Ab)s(ou)i(Salem,)h(W.)f(and)g(F) -8 b(r\177)-49 b(ohlic)m(h,)37 b(J.:)50 b(Status)36 b(of)g(the)g (fundamen)m(tal)h(la)m(ws)714 3916 y(of)32 b(thermo)s(dynamics,)j(in)e (preparation)p Black 324 4118 a([A-SF2])p Black 63 w(Ab)s(ou)24 b(Salem,W.)i(and)f(F)-8 b(r\177)-49 b(ohlic)m(h,)27 b(J.:)39 b(Adiabatic)25 b(theorems)h(and)f(rev)m(ersible)714 4238 y(isothermal)33 b(pro)s(cesses,)i(Lett.)e(Math.)g(Ph)m(ys.)h Fq(72)p FB(,)f(153-163)e(\(2005\))p Black 324 4440 a([BFS])p Black 149 w(Bac)m(h,)43 b(V.,)h(F)-8 b(r\177)-49 b(ohlic)m(h,)43 b(J.)e(and)g(Sigal,)h(I.M.:)61 b(Return)41 b(to)g(Equilibrium,)j(J.)714 4560 y(Math.)33 b(Ph)m(ys.)h Fq(41)k(no)f(6)p FB(,)c(3985-4061)d (\(2000\))p Black 324 4761 a([BR])p Black 195 w(Bratteli,)62 b(O.)57 b(and)f(Robinson,)63 b(D.:)90 b(Op)s(erator)56 b(Algebras)h(and)f(Quan-)714 4882 y(tum)40 b(Statistical)f(Mec)m (hanics)j(1,2,)f(T)-8 b(exts)40 b(and)g(Monographs)f(in)h(Ph)m(ysics,) 714 5002 y(Springer-V)-8 b(erlag)33 b(Berlin,)g(1987)p Black 1894 5251 a(37)p Black eop end %%Page: 38 38 TeXDict begin 38 37 bop Black Black Black 324 548 a FB([D])p Black 261 w(Donald,)31 b(M.J.)i(:)43 b(Relativ)m(e)32 b(Hamiltonians)h(whic)m(h)g(are)f(not)f(b)s(ounded)i(from)714 668 y(ab)s(o)m(v)m(e,)g(J.)g(F)-8 b(unc.)33 b(Anal.)g Fq(91)p FB(,)g(143)e(\(1990\))p Black 324 872 a([DJP])p Black 145 w(Derezi)s(\023)-51 b(nski,)35 b(J.,)g(Jaksi)m(\023)-46 b(c,)36 b(V.)e(and)g(Pillet,)i(C.-A.:)46 b(P)m(erturbation)35 b(theory)g(of)714 992 y Fy(W)820 956 y Ft(\003)859 992 y FB(-dynamics,)c(Liouvilleans,)g(and)e(KMS-states,)h(Rev.)f(Math.)g (Ph)m(ys.)h Fq(15)p FB(,)714 1112 y(447-489)h(\(2003\))p Black 324 1316 a([FMSUe])p Black 49 w(F)-8 b(r\177)-49 b(ohlic)m(h,)36 b(J.,)f(Merkli,)h(M.,)f(Sc)m(h)m(w)m(arz,)i(S.,)e(and)g (Ueltsc)m(hi,)h(D.:)47 b(Statistical)714 1436 y(mec)m(hanics)29 b(of)d(thermo)s(dynamic)j(pro)s(cesses,)h(in)d Fu(A)j(gar)-5 b(den)29 b(of)g(quanta)p FB(,)f(345-)714 1557 y(363,)k(W)-8 b(orld)32 b(Sci.)i(Publishing,)g(Riv)m(er)g(Edge,)f(New)g(Jersey)-8 b(,)34 b(2003)p Black 324 1760 a([Ho])p Black 214 w(Ho)m(wland,)54 b(J.S.:)78 b(Stationary)50 b(scattering)g(theory)g(for)f(time)h(dep)s (enden)m(t)714 1880 y(Hamiltonians,)33 b(Math.)g(Ann.)g Fq(207)p FB(,)g(315-335)e(\(1974\))p Black 324 2084 a([HP])p Black 197 w(Hunzik)m(er,)42 b(W.)e(and)f(Pillet,)i(C.-A.:)56 b(Degenerate)40 b(asymptotic)g(p)s(erturba-)714 2204 y(tion)32 b(theory)-8 b(,)34 b(Comm)m(un.)g(Math.)f(Ph)m(ys.)h Fq(90)p FB(,)f(219)f(\(1983\))p Black 324 2408 a([Hu])p Black 209 w(Hunzik)m(er,)80 b(W.:)117 b(Notes)70 b(on)f(asymptotic)i(p) s(erturbation)e(theory)h(for)714 2528 y(Sc)m(hr\177)-49 b(odinger)53 b(eigen)m(v)-5 b(alue)54 b(problems,)59 b(Helv.)53 b(Ph)m(ys.)i(Acta)d Fq(61)p FB(,)57 b(257-304)714 2648 y(\(1988\))p Black 324 2852 a([JP1])p Black 171 w(Jaksi)m(\023)-46 b(c,)40 b(V.)d(and)g(Pillet,)j(C.A.:)53 b(On)37 b(a)g(Mo)s(del)h(for)f(Quan)m(tum)g(F)-8 b(riction)37 b(I)s(I.)714 2972 y(F)-8 b(ermi's)29 b(Golden)g(Rule)g(and)g(Dynamics)h (at)f(P)m(ositiv)m(e)i(T)-8 b(emp)s(erature,)31 b(Com-)714 3093 y(m)m(un.)j(Math.)e(Ph)m(ys.)j Fq(176)p FB(,)e(619-644)d(\(1996\)) p Black 324 3296 a([JP2])p Black 171 w(Jaksi)m(\023)-46 b(c,)55 b(V.)49 b(and)g(Pillet,)54 b(C.A.:)78 b(On)49 b(a)g(Mo)s(del)g(for)g(Quan)m(tum)h(F)-8 b(riction)714 3416 y(I)s(I)s(I.)30 b(Ergo)s(dic)g(Prop)s(erties)i(of)d(the)i (Spin-Boson)f(System,)j(Comm)m(un.)e(Math.)714 3537 y(Ph)m(ys.)j Fq(178)p FB(,)f(627-651)e(\(1996\))p Black 324 3740 a([JP3])p Black 171 w(Jaksi)m(\023)-46 b(c,)32 b(V.)e(and)g(Pillet,)h(C.-A.:)43 b(Non-equilibrium)31 b(steady)h(states)e(of)g(\014nite)714 3861 y(quan)m(tum)43 b(systems)h(coupled)f(to)f(thermal)g(reserv)m (oirs,)47 b(Comm)m(un.)c(Math.)714 3981 y(Ph)m(ys.)34 b Fq(226)p FB(,)f(131-162)e(\(2002\))p Black 324 4184 a([JP4])p Black 171 w(Jaksi)m(\023)-46 b(c,)33 b(V.)f(and)g(Pillet,)h (C.-A.:)43 b(A)32 b(note)g(on)f(the)h(en)m(trop)m(y)i(pro)s(duction)e (for-)714 4305 y(m)m(ula,)e(Adv)-5 b(ances)30 b(in)f(di\013eren)m(tial) h(equations)g(and)f(mathematical)g(ph)m(ysics,)714 4425 y(175-180,)52 b(Con)m(temp.)f(Math.)f Fq(327)p FB(,)k(American)d (Mathematical)f(So)s(ciet)m(y)-8 b(,)714 4545 y(Pro)m(vidence,)35 b(RI,)e(2003)p Black 324 4749 a([Ka1])p Black 162 w(Kato,)24 b(T.:)38 b(P)m(erturbation)24 b(theory)e(for)g(linear)h(op)s(erators,)h (Berlin:)39 b(Springer,)714 4869 y(1980)p Black 1894 5251 a(38)p Black eop end %%Page: 39 39 TeXDict begin 39 38 bop Black Black Black 324 548 a FB([Ka2])p Black 162 w(Kato,)39 b(T.:)56 b(Linear)39 b(ev)m(olution)h(equations)g (of)e(h)m(yp)s(erb)s(olic)i(t)m(yp)s(e,)h(I.J.)e(F)-8 b(ac.)714 668 y(Sci.)33 b(Univ.)h(T)-8 b(oky)m(o)33 b(Sect.)h(IA)f Fq(17)p FB(,)f(241-258)f(\(1970\))p Black 324 872 a([PW])p Black 170 w(Pusz,)48 b(W.)c(and)g(W)-8 b(orono)m(wicz,)48 b(S.L.:)67 b(P)m(assiv)m(e)46 b(states)f(and)f(KMS)h(states)714 992 y(for)39 b(general)h(quan)m(tum)h(systems,)j(Comm)m(un.)d(Math.)f (Ph)m(ys.)i Fq(58)p FB(,)f(273-290)714 1112 y(\(1978\))p Black 324 1316 a([RS1,2])p Black 85 w(Reed,)70 b(M.)63 b(and)f(Simon,)70 b(B.:)103 b(Metho)s(ds)63 b(of)f(Mo)s(dern)h (Mathematical)714 1436 y(Ph)m(ysics,)29 b(V)-8 b(ol.)26 b(I)f(\(F)-8 b(unctional)25 b(Analysis\),)k(V)-8 b(ol.)25 b(I)s(I)g(\(F)-8 b(ourier)25 b(Analysis,)k(Self-)714 1557 y(Adjoin)m(tness\),)34 b(Academic)g(Press,)h(New)e(Y)-8 b(ork)33 b(1975)p Black 324 1760 a([Rud])p Black 156 w(Rudin,)48 b(W.:)69 b(Real)45 b(and)g(Complex)h(Analysis,)k(3rd)45 b(ed.,)j(Mc-Gra)m(w-Hill,)714 1880 y(New)33 b(Y)-8 b(ork,)33 b(1987)p Black 324 2084 a([Y)-8 b(a1])p Black 173 w(Y)g(a)5 b(jima,)40 b(K.:)56 b(Scattering)39 b(theory)g(for)f(Sc)m(hr\177)-49 b(odinger)40 b(equations)g(with)f(p)s(o-)714 2204 y(ten)m(tials)34 b(p)s(erio)s(dic)f(in)f(time,)i(J.)e(Math.)h(So)s(c.)g(Japan)f Fq(29)p FB(,)h(729-743)e(\(1977\))p Black 324 2408 a([Y)-8 b(a2])p Black 173 w(Y)g(a)5 b(jima,)27 b(K.:)40 b(Resonances)27 b(for)e(A)m(C-Stark)h(e\013ect,)i(Comm)m(un.)f(Math.)f(Ph)m(ys.)714 2528 y Fq(87)p FB(,)33 b(331-352)d(\(1982\))p Black 324 2731 a([Y)-8 b(o])p Black 222 w(Y)g(osida,)42 b(K.:)58 b(F)-8 b(unctional)40 b(Analysis,)k(6th)39 b(ed.,)k(Springer-V)-8 b(erlag,)42 b(Berlin,)714 2852 y(1998)p Black 1894 5251 a(39)p Black eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0512221319688--