Anderson localization for the band model

  • J. Bourgain
  • S. Jitomirskaya
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1745)

Abstract

In this paper, we show how the methods from [B-G] may be adapted to establish Anderson localization for quasi-periodic lattice Schrödinger operators corresponding to the band model ℤ × {1, ..., b}. Recall that ‘Anderson localization’ means pure point spectrum with exponentially decaying eigenfunctions. We also discuss the issue of dynamical localization.

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References

  1. [B-G]
    Bourgain J., Goldstein M. (1999) On non-perturbative localization with quasiperiodic potential. Preprint. Annals of Math., to appearGoogle Scholar
  2. [B-G-S]
    Bourgain J., Goldstein M., Schlag W. (2000) Anderson localization for Schrödinger operators on ℤ with potentials given by the skew-shift. PreprintGoogle Scholar
  3. [J-L]
    Jitomirskaya S., Last Y. (1999) Power Law subordinary and singular spectra II, Line operators. CMP, to appearGoogle Scholar

Copyright information

© Springer-Verlag 2000

Authors and Affiliations

  • J. Bourgain
    • 1
  • S. Jitomirskaya
    • 2
  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.University of CaliforniaIrvineUSA

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