Communications in Mathematical Physics

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

Spectral behavior of quasi periodic potentials

  • P. Sarnak


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Spectral Property 
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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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