20 citations · 67 across the 15 of their papers we have counts for
17 papers
Continuum limit of discretized matrix-valued Fourier multipliers
Ruben Karapetyan, Matěj Tušek
Building upon a recent result by H. Cornean, H. Garde, and A. Jensen concerning continuum limits of discrete Dirac operators, we extend the analysis to a wide class of block operat…
Non-self-adjoint Dirac operators on graphs
Markus Holzmann, Václav Růžek, Matěj Tušek
In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framewo…
Two-dimensional Schrödinger operators with non-local singular potentials
Lukáš Heriban, Markus Holzmann, Christian Stelzer-Landauer +2
In this paper we introduce and study a family of self-adjoint realizations of the Laplacian in with a new type of transmission conditions along a closed bi-Lips…
Two-dimensional Dirac operators with general -shell interactions supported on a straight line
Jussi Behrndt, Markus Holzmann, Matěj Tušek
In this paper the two-dimensional Dirac operator with a general hermitian -shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectr…
Non-self-adjoint relativistic point interaction in one dimension
Lukáš Heriban, Matěj Tušek
The one-dimensional Dirac operator with a singular interaction term which is formally given by , where is an arbitrary matrix and $δ…
Spectral transition for Dirac operators with electrostatic -shell potentials supported on the straight line
Jussi Behrndt, Markus Holzmann, Matěj Tušek
In this note the two dimensional Dirac operator with an electrostatic -shell interaction of strength supported on a straight line is studied. We observe a…
Location of hot spots in thin curved strips
David Krejcirik, Matěj Tušek
The maxima and minima of Neumann eigenfunctions of thin tubular neighbourhoods of curves on surfaces are located in terms of the maxima and minima of Neumann eigenfunctions of the…
Dispersionless wave packets in Dirac materials
Vit Jakubsky, Matej Tusek
We show that a wide class of quantum systems with translational invariance can host dispersionless, soliton-like, wave packets. We focus on the setting where the effective, two-dim…
On an extension of the Iwatsuka model
Matej Tusek
We prove absolute continuity for an extended class of two-dimensional magnetic Hamiltonians that were initially studied by A. Iwatsuka. In particular, we add an electric field that…
Nodal sets of thin curved layers
David Krejcirik, Matej Tusek
This paper is concerned with the location of nodal sets of eigenfunctions of the Dirichlet Laplacian in thin tubular neighbourhoods of hypersurfaces of the Euclidean space of arbit…
The magnetic Laplacian in shrinking tubular neighbourhoods of hypersurfaces
David Krejcirik, Nicolas Raymond, Matej Tusek
The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance bet…
Atoms confined by very thin layers
Matej Tusek
The Hamiltonian of an atom with electrons and a fixed nucleus of infinite mass between two parallel planes is considered in the limit when the distance between the planes t…
A New Estimate on the Two-Dimensional Indirect Coulomb Energy
Rafael D. Benguria, Pablo Gallegos, Matej Tusek
We prove a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound…
On the two-dimensional Coulomb-like potential with a central point interaction
P. Duclos, P. Stovicek, M. Tusek
In the first part of the paper, we introduce the Hamiltonian , Z>0, as a selfadjoint operator in . A general central point interaction combined with…
On the Spectrum of a Quantum Dot with Impurity in the Lobachevsky Plane
P. Stovicek, M. Tusek
A model of a quantum dot with impurity in the Lobachevsky plane is considered. Relying on explicit formulae for the Green function and the Krein function which have been derive…
On the harmonic oscillator on the Lobachevsky plane
P. Stovicek, M. Tusek
We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential where is the curvature radius and is the geodesic d…
A Quantum Dot with Impurity in the Lobachevsky Plane
V. Geyler, P. Stovicek, M. Tusek
The curvature effect on a quantum dot with impurity is investigated. The model is considered on the Lobachevsky plane. The confinement and impurity potentials are chosen so that th…