Exponential Dynamical Localization: Criterion and Applications

Abstract

We give a criterion for exponential dynamical localization in expectation (EDL) for ergodic families of operators acting on ${\ell }^2({\mathbb{Z}}^d)$. As applications, we prove EDL for a class of quasi-periodic long-range operators on ${\ell }^2({\mathbb{Z}}^d)$.