Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators

Jean Bourgain; Wei-Min Wang

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arXiv · math/0210336

Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators

Jean Bourgain·Wei-Min Wang

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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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Jean Bourgain, Wei-Min Wang. 2002-10-22. Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators. https://arxiv.org/abs/math/0210336

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