Proof of dynamical localization for perturbations of discrete 1D Schrödinger operators with uniform electric fields
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We present a proof of discrete spectrum and dynamical localization for small perturbations of discrete one-dimensional Schrödinger operators with uniform electric fields. The proof of dynamical localization is based on the KAM technique.
KeywordsDynamical localization Pure point spectrum Discrete Schrödinger operators Electric fields KAM technique
Mathematics Subject Classification47B39 47N50 81Q15
MP was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Brazilian agency). CRdO thanks partial support by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazilian agency, Universal Project 41004/2014-8).
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