Related papers: Absolutely continuous spectrum for the isotropic M…
We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.
In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell…
The paper contains a brief description of a simplified version of A. Sobolev's proof of absolute continuity of spectra of periodic magnetic Schr\"{o}dinger operators. This approach is applicable to all periodic elliptic operators known to…
We study the Schr\"odinger operator on $L_2(\mathbb R^3)$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the (appropriately defined) flux of the magnetic…
It is proven that the absolutely continuous spectrum of matrix Schr\"{o}dinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The…
In this paper we find a new condition on a real periodic potential for which the self-adjoint Schr\"odinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on…
The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…
I prove that quasi-periodic Schr\"odinger operators in arbitrary dimension have some absolutely continuous spectrum.
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 in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of…
We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity $\varepsilon$, permeability $\mu$ and conductivity $\sigma$, on finitely connected unbounded domains. The main result is…
We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially supported by $[0,\infty)$ for almost every $t$.
This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are…
We show that a large class of limit-periodic Schr\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative…
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 a family of multi-dimensional Schr\"odinger operators $-\Delta+t V$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the…
The Maxwell operator in a 3D cylinder is considered. The coefficients are assumed to be scalar functions depending on the longitudinal variable only. Such operator is represented as a sum of countable set of matrix differential operators of…
We consider a family of random Schr\"odinger operators on the discrete strip with decaying random $\ell^2$ matrix potential. We prove that the spectrum is almost surely pure absolutely continuous, apart from random, possibly embedded…
We prove that 3-dimensional Schrodinger operator with slowly decaying potential has an absolutely continuous spectrum that fills the positive half-line. The asymptotics of Green's function is obtained as well.
We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schr\"odinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and…