138 citations · 1.3k across the 90 of their papers we have counts for
34 papers · 1 filter
Bound states in soft quantum layers
David Krejcirik, Jan Kriz
We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel…
On the two-dimensional quantum confined Stark effect in strong electric fields
Horia Cornean, David Krejcirik, Thomas Garm Pedersen +2
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity…
Pseudomodes for non-self-adjoint Dirac operators
David Krejcirik, Tho Nguyen Duc
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large p…
Soft quantum waveguides with an explicit cut-locus
Sylwia Kondej, David Krejcirik, Jan Kriz
We consider two-dimensional Schroedinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve composed of a circular ar…
Bound states in semi-Dirac semi-metals
David Krejcirik, Pedro. R. S. Antunes
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spect…
Effective quantum dynamics on the Möbius strip
Tomáš Kalvoda, David Krejcirik, Katerina Zahradova
The Laplace-Beltrami operator in the curved Möbius strip is investigated in the limit when the width of the strip tends to zero. By establishing a norm-resolvent convergence, it is…
Quantum strips in higher dimensions
David Krejcirik, Katerina Zahradova
We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotica…
Absolute continuity of the spectrum in a twisted Dirichlet-Neumann waveguide
Philippe Briet, Jaroslav Dittrich, David Krejcirik
Quantum waveguide with the shape of planar infinite straight strip and combined Dirichlet and Neumann boundary conditions on the opposite half-lines of the boundary is considered.…
Spectral analysis of sheared nanoribbons
Philippe Briet, Hamza Abdou Soimadou, David Krejcirik
We investigate the spectrum of the Dirichlet Laplacian in a unbounded strip subject to a new deformation of "shearing": the strip is built by translating a segment oriented in a co…
The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
David Krejcirik, Vladimir Lotoreichik, Miloslav Znojil
We propose a unique way how to choose a new inner product in a Hilbert space with respect to which an originally non-self-adjoint operator similar to a self-adjoint operator become…
Complex magnetic fields: An improved Hardy-Laptev-Weidl inequality and quasi-self-adjointness
David Krejcirik
We show that allowing magnetic fields to be complex-valued leads to an improvement in the magnetic Hardy-type inequality due to Laptev and Weidl. The proof is based on the study of…
Reduction of dimension as a consequence of norm-resolvent convergence and applications
David Krejcirik, Nicolas Raymond, Julien Royer +1
This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The effic…
Asymptotic spectral analysis in colliding leaky quantum layers
Sylwia Kondej, David Krejcirik
We consider the Schroedinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properti…
A lower bound to the spectral threshold in curved quantum layers
Pedro Freitas, David Krejcirik
We derive a lower bound to the spectral threshold of the Dirichlet Laplacian in tubular neighbourhoods of constant radius about complete surfaces. This lower bound is given by the…
Magnetic effects in curved quantum waveguides
David Krejcirik, Nicolas Raymond
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to…
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…
On the metric operator for the imaginary cubic oscillator
Petr Siegl, David Krejcirik
We show that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator…
Perfect transmission scattering as a PT-symmetric spectral problem
H. Hernandez-Coronado, D. Krejcirik, P. Siegl
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for underst…
PT-symmetric models in curved manifolds
David Krejcirik, Petr Siegl
We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary…
Non-Hermitian spectral effects in a PT-symmetric waveguide
David Krejcirik, Milos Tater
We present a numerical study of the spectrum of the Laplacian in an unbounded strip with PT-symmetric boundary conditions. We focus on non-Hermitian features of the model reflected…
Twisting versus bending in quantum waveguides
David Krejcirik
We make an overview of spectral-geometric effects of twisting and bending in quantum waveguides modelled by the Dirichlet Laplacian in an unbounded three-dimensional tube of unifor…
Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
David Krejcirik
In a previous paper (arXiv:math-ph/0604055) we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed formula for the metric operat…
PT-symmetric waveguides
Denis Borisov, David Krejcirik
We introduce a planar waveguide of constant width with non-Hermitian PT-symmetric Robin boundary conditions. We study the spectrum of this system in the regime when the boundary co…
Waveguides with combined Dirichlet and Robin boundary conditions
Pedro Freitas, David Krejcirik
We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variabl…