Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators

2002/10/22 by Jean Bourgain, Bourgain, Jean, Wei-Min Wang +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.math/0210336

37 pgs

arxiv created 2002/10/22 · arxiv updated 2009/11/30

Abstract

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 Fröhlich-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 Schrödinger equations.

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