Related papers: Soft quantum waveguides with an explicit cut-locus
The paper is devoted to the study of the essential spectrum of discrete Schr\"{o}dinger operators on the lattice $\mathbb{Z}^{N}$ by means of the limit operators method. This method has been applied by one of the authors to describe the…
In this study, we have performed a detailed investigation of the electronic properties of a core/shell/well/shell multi-layered spherical quantum dot, such as energy eigenvalues, wave functions, electron probability distribution and binding…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
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 asymptotically flat. If the Gauss curvature of the strip equals zero,…
Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found…
The spectral properties of two-dimensional Schr\"odinger operators with $\delta'$-potentials supported on star graphs are discussed. We describe the essential spectrum and give a complete description of situations in which the discrete…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
We consider the cubic nonlinear Schr{\"o}dinger equation on the spatial domain $\mathbb{R}\times \mathbb{T}^d$, and we perturb it with a convolution potential. Using recent techniques of Hani-Pausader-Tzvetkov-Visciglia, we prove a modified…
We consider one dimensional Schr\"{o}dinger operators $H_\lambda=-\frac{d^2}{dx^2}+U+ \lambda V_\lambda$ with nonlinear dependence on the parameter $\lambda$ and study the small $\lambda$ behaviour of eigenvalues. The potentials $U$ and…
Derivation of tight-binding model from Schroedinger formalism for various topologies of position-based semiconductor qubits is presented in this work in case of static and time-dependent electric fields. Simplistic tight-binding model…
In this paper we study absence of embedded eigenvalues for Schr\"odinger operators on non-compact connected Riemannian manifolds. A principal example is given by a manifold with an end (possibly more than one) in which geodesic coordinates…
The spectrum of the Laplace operator in a curved strip of constant width built along an infinite plane curve, subject to three different types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is…
We investigate the nonrelativistic quantum dynamics of a spinless particle in a screw-type spacetime endowed with two independent twist controls that interpolate between a pure screw dislocation and a homogeneous twist. From the induced…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schr\"{o}dinger operator acting on a class of graphs. In particular, we derive tight bounds for the gap of Schr\"{o}dinger operators with convex…
We survey results that have been obtained for self-adjoint operators, and especially Schr\"odinger operators, associated with mathematical models of quasicrystals. After presenting general results that hold in arbitrary dimensions, we focus…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called…
We study the spectral properties of discrete Schr\"odinger operator $$ \widehat H_\mu=\widehat H_0 + \mu \widehat{V},\qquad \mu\ge0, $$ associated to a one-particle system in $d$-dimensional lattice $\mathbb{Z}^d, $ $d=1,2,$ where the…
We study the long time evolution of internal waves in two dimensional subcritical channels with flat horizontal ends. We show the leading profiles of solutions are the outgoing solutions to the stationary equations. This is done by showing…