Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators

Details Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators

2002-10-22

arxiv.org/abs/math/0210336v1

Mathematics

Spectral Theory

37 pgs

Scientific paper

We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in $\Bbb Z^d$ is {\it stable} under localized time-quasi-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The main tools are the Fr\"ohlich-Spencer mechanism for the random component and the Bourgain-Goldstein-Schlag mechanism for the quasi-periodic component. The formulation of this problem is motivated by questions of Anderson localization for non-linear Schr\"odinger equations.

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