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

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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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Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    S. Jitomirskaya & B. Simon

  2. Division of Physics, Mathematics and Astronomy, California Institute of Technology 253-37, 91125, Pasadena, CA, USA

    S. Jitomirskaya & B. Simon

Authors
  1. S. Jitomirskaya
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  2. B. Simon
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Additional information

Communicated by T. Spencer

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.

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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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  • DOI: https://doi.org/10.1007/BF02099743

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