Localização dinâmica para perturbações de operadores de Schrödinger discretos com campo elétrico

Abstract

We study the spectrum and the dynamical localization of some discrete quantum systems with uniform electric fields under suitable perturbations with exponential decay in the matrix elements. We consider three particular situations. (1) In the first situation, we study the discrete Schr¨odinger operator in one dimension under bounded perturbations. (2) We also consider the discrete 2D Schr¨odinger operator. (3) Finally we study the 2D case under time periodic perturbation. The proofs are based on the KAM technique.