181 citations · 3.2k across the 184 of their papers we have counts for
191 papers
Tunneling in soft waveguides:closing a book
Pavel Exner, David Spitzkopf
We investigate the spectrum of a soft quantum waveguide in two dimensions of the generalized `bookcover' shape, that is, Schrödinger operator with the potential in the form of a di…
Geometry effects in quantum dot families
Pavel Exner
We consider Schrödinger operators in , with the interaction in the form on an array of potential wells, each on them having rotational symmetry, arrange…
Bound States in Bent Soft Waveguides
Pavel Exner, Semjon Vugalter
The aim of this paper is to show that a two-dimensional Schrödinger operator with the potential in the form of a `ditch' of a fixed profile can have a geometrically induced discret…
Magnetic square lattice with vertex coupling of a preferred orientation
Marzieh Baradaran, Pavel Exner, Jiří Lipovský
We analyze a square lattice graph in a magnetic field assuming that the vertex coupling is of a particular type violating the time reversal invariance. Calculating the spectrum num…
Bound states of weakly deformed soft waveguides
Pavel Exner, Sylwia Kondej, Vladimir Lotoreichik
In this paper we consider the two-dimensional Schrödinger operator with an attractive potential which is a multiple of the characteristic function of an unbounded strip-shaped regi…
Spectral transition model with the general contact interaction
Pavel Exner, Jiří Lipovský
Using a technique introduced by Sergei Naboko, we analyze a generalization of the parameter-controlled model of spectral transition, originally proposed by Smilansky and Solomyak,…