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Communications in Mathematical Physics

, Volume 84, Issue 3, pp 377–401 | Cite as

Spectral behavior of quasi periodic potentials

  • P. Sarnak
Article

Abstract

Spectral properties of Schrödinger operators of the typeHɛ=−Δ+ɛV, where Δ is the Laplacian,V a quasiperiodic potential and ɛ a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small ɛ a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as ɛ is increased.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Spectral Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • P. Sarnak
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew YorkUSA

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