Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators

Abstract

We prove that one-dimensional Schrödinger operators with even almost periodic potential have no point spectrum for a denseG δ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a denseG δ in θ even if the frequency is an irrational with good Diophantine properties.

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This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.

Communicated by T. Spencer

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Jitomirskaya, S., Simon, B. Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators. Commun.Math. Phys. 165, 201–205 (1994). https://doi.org/10.1007/BF02099743

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Keywords

  • Neural Network
  • Statistical Physic
  • Complex System
  • Hull
  • Nonlinear Dynamics