University of Hradec Králové

output

20002026

most citedExperimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption

85 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

Showing math-phShow all

29 papers · 1 filter

math-ph2025★ 1 cited

Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint

Miloslav Znojil

A family of discrete Schrödinger equations with imaginary potentials $V (x)$ is studied. Inside the domain $D$ of unitarity-compatible values of $V (x)$ , the reality of all of…

math-ph2025

Mutual compatibility/incompatibility of quasi-Hermitian quantum observables

Miloslav Znojil

In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_{j} \neq = A_{j}^{†}$ , $j = 1, 2, \dots, K$ . In principle, the standa…

math-ph2025★ 4 cited

Complex tridiagonal quantum Hamiltonians and matrix continued fractions

Miloslav Znojil

Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians $H$ with complex energy eigenvalues are considered. The method of evaluation of quantities $σ_{n}$ known…

math-ph2024★ 5 cited

A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians

Bijan Bagchi, Aritra Ghosh, Miloslav Znojil

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep conne…

math-ph2023★ 2 cited

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…

math-ph2022★ 2 cited

Interference of non-Hermiticity with Hermiticity at exceptional points

Miloslav Znojil

A family of non-Hermitian but $P T -$ symmetric $2 J$ by $2 J$ toy-model tridiagonal-matrix Hamiltonians $H^{(2 J)} = H^{(2 J)} (t)$ with $J = K + M = 1, 2, \dots$ and $t < J^{2}$ is studied, fo…

math-ph2022★ 3 cited

Magnetic ring chains with vertex coupling of a preferred orientation

Marzieh Baradaran, Pavel Exner, Jiri Lipovsky

We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex cou…

math-ph2021★ 6 cited

Kagome network with vertex coupling of a preferred orientation

Marzieh Baradaran, Pavel Exner

We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at the…

math-ph2021★ 10 cited

Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians

Miloslav Znojil

A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_…

math-ph2020★ 3 cited

Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation

Miloslav Znojil

Non-Hermitian but $P T -$ symmetric quantum system of an $N -$ plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H (γ, v, c)$ is picked up, in its special e…

math-ph2020★ 12 cited

Perturbation theory near degenerate exceptional points

Miloslav Znojil

In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the pertur…

math-ph2020★ 10 cited

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…

math-ph2020★ 9 cited

Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations

D. I. Borisov, D. A. Zezyulin, M. Znojil

We consider the operator $H = H^{'} - \frac{\partial ^{2}}{\partial x _{d}^{2}} on ω \times R$ subject to the Dirichlet or Robin condition, where a dom…

math-ph2020★ 5 cited

Differential invariants of measurements, and their connection to central moments

Eivind Schneider

Due to the principle of minimal information gain, the measurement of points in an affine space $V$ determines a Legendrian submanifold of $V \times V^{*} \times R$ . Such Lege…

math-ph2020★ 13 cited

Topological bulk-edge effects in quantum graph transport

Pavel Exner, Jiri Lipovsky

We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive…

math-ph2019★ 9 cited

Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials

D. I. Borisov, D. A. Zezyulin

We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large d…

math-ph2019★ 6 cited

Spectral determinant for the damped wave equation on an interval

Pedro Freitas, Jiří Lipovský

We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. T…

math-ph2019★ 6 cited

Spacing gain and absorption in a simple $P T$ -symmetric model: spectral singularities and ladders of eigenvalues and resonances

D. I. Borisov, D. A. Zezyulin

We consider a parity-time ( $P T$ -) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Sc…

math-ph2019★ 3 cited

A Gelfand-Levitan trace formula for generic quantum graphs

Pedro Freitas, Jiri Lipovsky

We formulate and prove a Gelfand-Levitan trace formula for general quantum graphs with arbitrary edge lengths and coupling conditions which cover all self-adjoint operators on quan…

math-ph2018★ 3 cited

Smilansky-Solomyak model with a $δ^{'}$ -interaction

Pavel Exner, Jiří Lipovský

We investigate a strongly singular version of the model of irreversible dynamics proposed by Smilansky and Solomyak in which the interaction responsible for an abrupt change of the…

math-ph2017★ 8 cited

Asymptotics of resonances induced by point interactions

Jiri Lipovsky, Vladimir Lotoreichik

We consider the resonances of the self-adjoint three-dimensional Schrödinger operator with point interactions of constant strength supported on the set $X = {x_{n}}_{n = 1}^{N}$ . The…

math-ph2016★ 6 cited

Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics

Pavel Exner, Jiri Lipovsky

The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths…

math-ph2016★ 5 cited

Displaced harmonic oscillator $V \sim min [(x + d)^{2}, (x - d)^{2}]$ as a benchmark double-well quantum model

Miloslav Znojil

For the displaced harmonic double-well oscillator the existence of exact polynomial bound states at certain displacements $d$ is revealed. The $N -$ plets of these quasi-exactly so…

math-ph2016★ 4 cited

On Hopf algebroid structure of kappa-deformed Heisenberg algebra

Jerzy Lukierski, Zoran Škoda, Mariusz Woronowicz

The $(4 + 4)$ -dimensional $κ$ -deformed quantum phase space as well as its $(10 + 10)$ -dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the…

Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint

Mutual compatibility/incompatibility of quasi-Hermitian quantum observables

Complex tridiagonal quantum Hamiltonians and matrix continued fractions

A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians

Magnetic square lattice with vertex coupling of a preferred orientation

Interference of non-Hermiticity with Hermiticity at exceptional points

Magnetic ring chains with vertex coupling of a preferred orientation

Kagome network with vertex coupling of a preferred orientation

Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians

Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation

Perturbation theory near degenerate exceptional points

Soft quantum waveguides with an explicit cut-locus

Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations

Differential invariants of measurements, and their connection to central moments

Topological bulk-edge effects in quantum graph transport

Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials

Spectral determinant for the damped wave equation on an interval

Spacing gain and absorption in a simple PT-symmetric model: spectral singularities and ladders of eigenvalues and resonances

A Gelfand-Levitan trace formula for generic quantum graphs

Smilansky-Solomyak model with a δ′-interaction

Asymptotics of resonances induced by point interactions

Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics

Displaced harmonic oscillator V∼min[(x+d)2,(x−d)2] as a benchmark double-well quantum model

On Hopf algebroid structure of kappa-deformed Heisenberg algebra

Spacing gain and absorption in a simple $P T$ -symmetric model: spectral singularities and ladders of eigenvalues and resonances

Smilansky-Solomyak model with a $δ^{'}$ -interaction

Displaced harmonic oscillator $V \sim min [(x + d)^{2}, (x - d)^{2}]$ as a benchmark double-well quantum model