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Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 1525–1541 | Cite as

Proof of dynamical localization for perturbations of discrete 1D Schrödinger operators with uniform electric fields

  • César R. de OliveiraEmail author
  • Mariane Pigossi
Article

Abstract

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.

Keywords

Dynamical localization Pure point spectrum Discrete Schrödinger operators Electric fields KAM technique 

Mathematics Subject Classification

47B39 47N50 81Q15 

Notes

Acknowledgements

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticaUFSCarSão CarlosBrazil

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