Communications in Mathematical Physics

, Volume 168, Issue 3, pp 563–570 | Cite as

Anderson localization for the almost Mathieu equation: II. Point spectrum for λ>2

  • Svetlana Ya. Jitomirskaya
Article

Abstract

We prove that for any λ>2 and a.e. ω, θ the pure point spectrum of the almost Mathieu operator (H(θ)Ψ) n = Ψ n-1 + Ψ n+1 + λ cos(2π(θ +nω))Ψ n contains the essential closure\(\hat \sigma\) of the spectrum. Corresponding eigenfunctions decay exponentially. The singular continuous component, if it exists, is concentrated on a set of zero measure which is nowhere dense in\(\hat \sigma\).

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Svetlana Ya. Jitomirskaya
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA

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