 07261 Pavel Exner
 Leaky Quantum Graphs: A Review
(575K, LaTeX, amsproc.sty)
Oct 31, 07

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

Abstract. The aim of this review is to provide an overview of a recent work
concerning ``leaky'' quantum graphs described by Hamiltonians
given formally by the expression $\Delta \alpha \delta
(x\Gamma)$ with a singular attractive interaction supported by a
graphlike set in $\mathbb{R}^\nu,\: \nu=2,3$. We will explain how
such singular Schr\"odinger operators can be properly defined for
different codimensions of $\Gamma$. Furthermore, we are going to
discuss their properties, in particular, the way in which the
geometry of $\Gamma$ influences their spectra and the scattering,
strongcoupling asymptotic behavior, and a discrete counterpart to
leakygraph Hamiltonians using point interactions. The subject
cannot be regarded as closed at present, and we will add a list of
open problems hoping that the reader will take some of them as a
challenge.
 Files:
07261.src(
07261.comments ,
07261.keywords ,
leaky_newton.pdf.mm )