Communications in Mathematical Physics

, Volume 95, Issue 4, pp 401–425

An exactly solvable model of a multidimensional incommensurate structure

  • A. L. Figotin
  • L. A. Pastur
Article

Abstract

The paper considers the class of Schrödinger multidimensional discrete operators with quasi-periodic unbounded potential for which essentially complete spectral analysis may be carried out. In the case of sufficiently high incommensurability of almost-periods, the spectrum of such operators is found to be pure point and simple, the eigenfunctions exponentially localized and the low frequency conductivity exponentially small. In the one-dimensional case, for any incommensurability, the spectrum does not contain the absolutely continuous component, while for small incommensurability the spectrum is singular continuous.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • A. L. Figotin
    • 1
  • L. A. Pastur
    • 1
  1. 1.Institute for Low Temperature Physics and EngineeringUkrSSR Academy of SciencesKharkovUSSR

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