181 citations · 3.2k across the 184 of their papers we have counts for
6 papers · 1 filter
Schroedinger operators with singular interactions: a model of tunneling resonances
Pavel Exner, Sylwia Kondej
We discuss a generalized Schrödinger operator in , with an attractive singular interaction supported by a -dimensional hyperplane and a finite fami…
Convergence of spectra of graph-like thin manifolds
Pavel Exner, Olaf Post
We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator c…
Leaky quantum wire and dots: a resonance model
Pavel Exner, Sylwia Kondej
We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in with an attractive singular perturbation supported by a line a…
Absolute continuity in periodic thin tubes and strongly coupled leaky wires
Francois Bentosela, Pierre Duclos, Pavel Exner
Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or t…
Spectra of soft ring graphs
P. Exner, M. Tater
We discuss of a ring-shaped soft quantum wire modeled by interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines th…
Strong-coupling asymptotic expansion for Schrödinger operators with a singular interaction supported by a curve in
P. Exner, S. Kondej
We investigate a class of generalized Schrödinger operators in with a singular interaction supported by a smooth curve . We find a strong-coupling asymptotic…