 00248 Pavel Exner, David Krejcirik
 Waveguides coupled through a semitransparent barrier: a
BirmanSchwinger analysis
(92K, LaTeX)
May 30, 00

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The paper is devoted to a model of a mesoscopic
system consisting of a pair of parallel planar waveguides
separated by an infinitely thin semitransparent boundary modeled
by a transverse delta interaction. We develop the
BirmanSchwinger theory for the corresponding generalized
Schroedinger operator. The spectral properties become nontrivial
if the barrier coupling is not invariant with respect to
longitudinal translations, in particular, there are bound states
if the barrier is locally more transparent in the mean and the
coupling parameter reaches the same asymptotic value in both
directions along the guide axis. We derive the weakcoupling
expansion of the groundstate eigenvalue for the cases when the
perturbation is small in the supremum and the L^1norms. The
last named result applies to the situation when the support of the
leaky part shrinks: the obtained asymptotics differs from that of
a double guide divided by a pierced Dirichlet barrier. We also
derive an upper bound on the number of bound states.
 Files:
00248.tex