Anderson Localization for Time Quasi-Periodic Random Schrödinger and Wave Equations

Abstract

We prove that at large disorder, with large probability and for a corresponding set of Diophantine frequencies of large measure, Anderson localization in ℤ d is stable under localized time quasi-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The main tools are the Frohlich-Spencer mechanism for the random component and the Bourgain-Goldstein-Schlag mechanism for the quasi-periodic component. This paper paves the way for the construction of time quasi-periodic KAM type of solutions of non linear random Schrodinger equations in [BW].