Pavel Exner and Sylwia Kondej
Leaky quantum wire and dots: a resonance model
(36K, LaTeX)

ABSTRACT.  We discuss a model of a leaky quantum wire and a family
of quantum dots described by Laplacian in $L^2(\mathbb{R}^2)$ with
an attractive singular perturbation supported by a line and a
finite number of points. The discrete spectrum is shown to be
nonempty, and furthermore, the resonance problem can be explicitly
solved in this setting; by Birman-Schwinger method it is
reformulated into a Friedrichs-type model.