181 citations · 3.2k across the 184 of their papers we have counts for
33 papers · 1 filter
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…
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…
Magnetic transport in laterally coupled layers
Pavel Exner
We discuss magnetic transport in the system of two adjacent hard-wall layers exposed to a homogeneous field perpendicular to the layer plane and coupled laterally through a strip-s…
Spectral estimates for Dirichlet Laplacian on spiral-shaped regions
Diana Barseghyan, Pavel Exner
We derive spectral estimates of the Lieb-Thirring type for eigenvalues of Dirichlet Laplacians on strictly shrinking spiral-shaped domains.