Related papers: On the shape of spectra for non-self-adjoint perio…
We study the fractal dimension of the spectrum of a quasiperiodical Schrodinger operator associated to a sturmian potential. We consider potential defined with irrationnal number verifying a generic diophantine condition. We recall how…
We consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We determine trace formulas for the Schr\"odinger operators. The proof is based on the…
In this paper we study spectral properties of a family of quasi-periodic Schr\"odinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curve has a real branch that is extended along the momentum…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite…
In this paper, we develop a systematic framework to study the dispersion surfaces of Schr{\"o}dinger operators $ -\Delta + V$, where the potential $V \in C^\infty(\mathbb{R}^n,\mathbb{R})$ is periodic with respect to a lattice $\Lambda…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
In this article we present comparisons between the spectrum of a one-dimensional Schr\"odinger operator for a particular periodic potential and for its restriction to a finite number of sites. We deduce from this finite, but large, number…
This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…
In this paper we find explicit conditions on the periodic PT-symmetric complex-valued potential q for which the number of gaps in the real part of the spectrum of the one-dimensional Schrodinger operator L(q) is finite.
Spectral components of one-dimensional Schr\"odinger operator with complex potential are investigated. An effective upper bound for the total number of eigenvalues and spectral singularities is established. For dissipative Schr\"odinger…
This paper aims to investigate the pseudo-modes of the one-dimensional Schr\"odinger operator with complex potentials, focusing on the behavior of the resolvent norm along specific curves in the complex plane and assessing the stability of…
The subject of the paper are Schr\"odinger operators on tree graphs which are radial having the branching number $b_n$ at all the vertices at the distance $t_n$ from the root. We consider a family of coupling conditions at the vertices…
Spectral properties of Schr\"odinger operators on compact metric graphs are studied and special emphasis is put on differences in the spectral behavior between different classes of vertex conditions. We survey recent results especially for…
In this paper, we study spectral properties of a family of quasi-periodic Schrodinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curves are extended along the momentum direction. In the…
The spectrum of random ergodic Schr\"odinger-type operators is almost surely a deterministic subset of the real line. The random operator can be considered as a perturbation of a periodic one. As soon as the disorder is switched on via a…
We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum…
We consider Schr\"odinger operators $H^h = (ih d+{\bf A})^* (ih d+{\bf A})$ with the periodic magnetic field ${\bf B}=d{\bf A}$ on covering spaces of compact manifolds. Under some assumptions on $\bf B$, we prove that there are arbitrarily…
We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$, $n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric…
We consider the Schr\"odinger operator on the real line with a $N\ts N$ matrix valued periodic potential, N>1. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov…
We consider the self-adjoint third order operator with 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers the real line. We determine the high energy asymptotics of the periodic,…