Related papers: Low lying spectral gaps induced by slowly varying …

The spectral properties of the Schr\"odinger operator $T_ty= -y''+q_ty$ in $L^2(\R)$ are studied, with a potential $q_t(x)=p_1(x), x<0, $ and $q_t(x)=p(x+t), x>0, $ where $p_1, p$ are periodic potentials and $t\in \R$ is a parameter of…

We determine the low-energy behaviour of the scattering operator of two-dimensional Schr\"odinger operators with any type of obstructions at 0-energy. We also derive explicit formulas for the wave operators in the absence of p-resonances,…

We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…

We consider Schr\"odinger operators with periodic electric and magnetic potentials on periodic discrete graphs. The spectrum of such operators consists of an absolutely continuous (a.c.) part (a union of a finite number of non-degenerate…

We consider Schr\"odinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be…

In this work, we use regularized determinant approach to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schr\"odinger operator $(-i\nabla - \textbf{\textup{A}})^{2} - b$ in…

We study the regularity properties of the Hausdorff distance between spectra of continuous Harper-like operators. As a special case we obtain H\"{o}lder continuity of this Hausdorff distance with respect to the intensity of the magnetic…

We present general principles for the preservation of a.c. spectrum under weak perturbations. The Schrodinger operators on the strip and on the Caley tree (Bethe lattice) are considered.

Using a correspondence between the spectrum of the damped wave equation and non-self-adjoint Schroedinger operators, we derive various bounds on complex eigenvalues of the former. In particular, we establish a sharp result that the…

We describe a novel technique for creating an artificial magnetic field for ultra-cold atoms using a periodically pulsed pair of counter propagating Raman lasers that drive transitions between a pair of internal atomic spin states: a…

We show that spectral Hausdorff dimensional properties of discrete Schr\"oodinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations,…

We introduce an accurate non-Hermitian Schr\"odinger-type approximation of Bloch optical equations for two-level systems. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics in both weak…

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below…

We present a theoretical study of the bandstructure and Landau levels in bilayer graphene at low energies in the presence of a transverse magnetic field and Rashba spin-orbit interaction in the regime of negligible trigonal distortion.…

We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…

This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…

We consider the Schr\"odinger operator in two dimensions with a periodic potential and a strong constant magnetic field perturbed by slowly varying non-periodic scalar and vector potentials, $\phi(\epsilon x)$ and $A(\epsilon x)$, for…

We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition…

We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in…

We study the Schroedinger operator with a constant magnetic field in the exterior of a two-dimensional compact domain. Functions in the domain of the operator are subject to a boundary condition of the third type (Robin condition). In…