181 citations · 3.2k across the 184 of their papers we have counts for
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Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes
Pavel Exner, Diana Barseghyan
We investigate Dirichlet Laplacian in a straight twisted tube of a non-circular cross section, in particular, its discrete spectrum coming from a local slowdown of the twist. We pr…
Solvable models of resonances and decays
Pavel Exner
Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems wh…
Momentum operators on graphs
Pavel Exner
We discuss ways in which momentum operators can be introduced on an oriented metric graph. A necessary condition appears to the balanced property, or a matching between the numbers…
A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
Pavel Exner, Olaf Post
We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph…
Spectral estimates for Dirichlet Laplacians and Schroedinger operators on geometrically nontrivial cusps
Pavel Exner, Diana Barseghyan
The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions having infinite cusps which are geometrically nont…