Related papers: Positive Measure Spectrum for Schroedinger Operato…
Building on works of Berth\'e--Steiner--Thuswaldner and Fogg--Nous we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion.…
Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homogeneous magnetic field are considered. Analytic expressions are obtained for the energy spectrum of the two- and three-dimensional…
An upper estimate for the number of negative eigenvalues below the essential spectrum for the magnetic Schr\"odinger operator with Aharonov-Bohm magnetic field in a strip is obtained. Its further shown that the estimate does not hold in…
In this note we review spectral properties of magnetic random Schroedinger operators H_omega=H_0+V_omega + U_l + U_r defined on L^2(R x [-L/2,L/2],dx dy) with periodic boundary conditions along y. U_l and U_r are two confining potentials…
Under certain simplifying conditions we detect monotonicity properties of the ground-state energy and the canonical-equilibrium density matrix of a spinless charged particle in the Euclidean plane subject to a perpendicular, possibly…
We study relations between spectra of two operators that are connected to each other through some intertwining conditions. As application we obtain new results on the spectra of multiplication operators on $B(\cl H)$ relating it to the…
We consider decaying oscillatory perturbations of periodic Schr\"odinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variation condition at infinity and an $L^p$ decay condition. We…
We discuss discrete one-dimensional Schr\"odinger operators whose potentials are generated by an invertible ergodic transformation of a compact metric space and a continuous real-valued sampling function. We pay particular attention to the…
Schr\"odinger operators with potentials generated by primitive substitutions are simple models for one dimensional quasi-crystals. We review recent results on their spectral properties. These include in particular an algorithmically…
We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction…
We evaluate for the inhomogeneous static electric Sauter step potential the imaginary part of the emerging homogeneous in electric field effective Euler-Heisenberg-Schwinger action sourced by vacuum fluctuations of a charged particle with…
Schroedinger operators with certain Gaussian random potentials in multi-dimensional Euclidean space possess almost surely an absolutely continuous integrated density of states and no absolutely continuous spectrum at sufficiently low…
We consider parabolic Schr\"odinger type equations associated to fractional powers of uniformly elliptic 2m-order operators with constant coefficients. Potentials and initial data are considered in suitable Morrey spaces. By means of…
We study the eigenvalues of the magnetic Schroedinger operator associated with a magnetic potential A and a scalar potential q, on a compact Riemannian manifold M, with Neumann boundary conditions if the boundary is not empty. We obtain…
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant H\"older…
The Bethe-Sommerfeld conjecture states that the spectrum of the stationary Schrodinger operator with a periodic potential in dimensions higher than 1 has only finitely many gaps. After work done by many authors, it has been proven by now in…
We consider open manifolds which are interiors of a compact manifold with boundary, and Riemannian metrics asymptotic to a conformally cylindrical metric near the boundary. We show that the essential spectrum of the Laplace operator on…
We consider a 2D Schroedinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which…
We study the energy spectrum and wave packet dynamics of electrons in a two-dimensional periodic potential subject to a perpendicular spatially modulated magnetic field. We observe avoided band crossings, metal-insulator transitions, and…
We consider a $2d$ magnetic Schr\"odinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `Landau type' structure of spectral islands at the bottom of…