Related papers: Trace Formulae for quantum graphs with edge potent…
For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero…
We consider Schr\"odinger operators in $L^2(\mathrm{R}^\nu),\, \nu=2,3$, with the interaction in the form on an array of potential wells, each on them having rotational symmetry, arranged along a curve $\Gamma$. We prove that if $\Gamma$ is…
We provide a unified method to study the adjacency matrices of regular graphs (including infinite ones) using holomorphic functional calculus. By applying this calculus on a specific ellipse that contains the spectrum, we derive an…
The information content and properties of the cross section for atom scattering from a defect on a flat surface are investigated. Using the Sudden approximation, a simple expression is obtained that relates the cross section to the…
While many bounds have been proved for partial trace inequalities over the last decades for a large variety of quantities, recent problems in quantum information theory demand sharper bounds. In this work, we study optimal bounds for…
We consider discrete Schr\"odinger operators $H_{\mu Q}=\Delta+\mu Q$ with real periodic potentials $Q$ on periodic graphs, where $\Delta$ is the adjacency operator and $\mu\in\mathbb R$ is a coupling constant. The spectra of the operators…
We consider discrete Schr\"odinger operators with pattern Sturmian potentials. This class of potentials strictly contains the class of Sturmian potentials, for which the spectral properties of the associated Schr\"odinger operators are well…
The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED…
Based on our previous study [IS2] we develop fully the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic…
We study a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. These Scattering Quantum Walks model the discrete dynamics of a system on the edges of the graph, with a scattering process at…
We consider semiclassical Schr\"odinger operators acting in $L^2(\mathbb{R}^d)$ with $d\geq3$. For these operators we establish a sharp spectral asymptotics without full regularity. For the counting function we assume the potential is…
In the model suggested by Smilansky one studies an operator describing the interaction between a quantum graph and a system of $K$ one-dimensional oscillators attached at several different points in the graph. The present paper is the first…
Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…
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…
The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schr\"odinger operators with a $\delta$-potential. These operators arise by replacing…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…