40 citations · 107 across the 8 of their papers we have counts for
11 papers · 1 filter
Necklaces with interacting beads: isoperimetric problems
Pavel Exner
We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places identical point charges at a closed curve at the…
Approximations of permutation-symmetric vertex couplings in quantum graphs
Pavel Exner, Ondrej Turek
We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such condition…
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…
Large gaps in point-coupled periodic systems of manifolds
J. Bruening, P. Exner, V. A. Geyler
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the t…
Bound states due to a strong interaction supported by a curved surface
Pavel Exner, Sylwia Kondej
We study the Schrödinger operator in with a interaction supported by an infinite non-planar surface which is smooth, admits a global normal paramet…
Some properties of the one-dimensional generalized point interactions (a torso)
P. Exner, H. Grosse
This text is a part of an unfinished project which deals with the generalized point interaction (GPI) in one dimension. We employ two natural parametrizations, which are known but…