36 citations · 224 across the 24 of their papers we have counts for
20 papers · 1 filter
Resonances in a Dirichlet quantum waveguide coupled to a cavity
Sylwia Kondej, Nikoloz Kurtskhalia
We consider a Dirichlet waveguide in () with an attached cavity. We show that if the cavity admits a small gap, then the original embedded eigenvalues turn…
Fermi's golden rule in tunneling models with quantum waveguides perturbed by Kato class measures
Sylwia Kondej, Kacper Ślipko
In this paper we consider two dimensional quantum system with an infinite waveguide of the width and a transversally invariant profile. Furthermore, we assume that at a distant…
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…
Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction
Pavel Exner, Sylwia Kondej
We discuss the spectral properties of singular Schrödinger operators in three dimensions with the interaction supported by an equilateral star, finite or infinite. In the finite ca…
Scattering on leaky wires in dimension three
Pavel Exner, Sylwia Kondej
We consider the scattering problem for a class of strongly singular Schrödinger operators in which can be formally written as where $α\…
Straight quantum layer with impurities inducing resonances
Sylwia Kondej
We consider a straight three dimensional quantum layer with singular potential supported on a straight wire which is localized perpendicularly to the walls and connects them. We pr…
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…
Spectral asymptotics induced by approaching and diverging planar circles
Sylwia Kondej
We consider two dimensional system governed by the Hamiltonian with delta interaction supported by two concentric circles separated by distance . We analyze the asymptotics of t…
Gap asymptotics in a weakly bent leaky quantum wire
Pavel Exner, Sylwia Kondej
The main question studied in this paper concerns the weak-coupling behavior of the geometrically induced bound states of singular Schrödinger operators with an attractive inter…
A straight waveguide with a wire inducing resonances
Sylwia Kondej, Wiesław Leoński
We study a straight infinite planer waveguide with, so called, leaky wire attached to the walls of the waveguide. The wire is modelled by an attractive delta interaction supported…
Hiatus perturbation for a singular Schrödinger operator with an interaction supported by a curve in \mathbb{R}^3
Pavel Exner, Sylwia Kondej
We consider Schrödinger operators in with a singular interaction supported by a finite curve . We present a proper definition of the operators and study thei…
Spectral gap of segments of periodic waveguides
Sylwia Kondej, Ivan Veselic'
We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of per…
Lower bounds on the lowest spectral gap of singular potential Hamiltonians
Sylwia Kondej, Ivan Veselic'
We analyze Schrödinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at…
Scattering by local deformations of a straight leaky wire
Pavel Exner, Sylwia Kondej
We consider a model of a leaky quantum wire with the Hamiltonian in , where is a compact deformation of a straight line. The existence of wave operators…
Schroedinger operators with singular interactions: a model of tunneling resonances
Pavel Exner, Sylwia Kondej
We discuss a generalized Schrödinger operator in , with an attractive singular interaction supported by a -dimensional hyperplane and a finite fami…
Leaky quantum wire and dots: a resonance model
Pavel Exner, Sylwia Kondej
We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in with an attractive singular perturbation supported by a line a…
Strong-coupling asymptotic expansion for Schrödinger operators with a singular interaction supported by a curve in
P. Exner, S. Kondej
We investigate a class of generalized Schrödinger operators in with a singular interaction supported by a smooth curve . We find a strong-coupling asymptotic…
Bound states due to a strong interaction supported by a curved surface
Pavel Exner, Sylwia Kondej
We study the Schrödinger operator in with a interaction supported by an infinite non-planar surface which is smooth, admits a global normal paramet…
Curvature-induced bound states for a interaction supported by a curve in
Pavel Exner, Sylwia Kondej
We study the Laplacian in perturbed on an infinite curve by a interaction defined through boundary conditions which relate the corresponding generalized…
On Eigenvalues Problem for Self-adjoint Operators with Singular Perturbations
Sylwia Kondej
We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singula…