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Anderson Localization for the Almost Mathieu Equation, III. Semi-Uniform Localization, Continuity of Gaps, and Measure of the Spectrum

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Abstract:

We show that the almost Mathieu operator, , has semi-uniform (and thus dynamical) localization for λ > 15 and a.e. ω,θ. We also obtain a new estimate on gap continuity (in ω) for this operator with λ > 29 (or λ < 4/29), and use it to prove that the measure of its spectrum is equal to for λ in this range and all irrational ω's.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, CA 92697, USA, , , , , , US

    Svetlana Y. Jitomirskaya

  2. Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena,¶CA 91125, USA, , , , , , US

    Yoram Last

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  1. Svetlana Y. Jitomirskaya
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  2. Yoram Last
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Received: 7 July 1997 / Accepted: 15 September 1997

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Jitomirskaya, S., Last, Y. Anderson Localization for the Almost Mathieu Equation, III. Semi-Uniform Localization, Continuity of Gaps, and Measure of the Spectrum . Comm Math Phys 195, 1–14 (1998). https://doi.org/10.1007/s002200050376

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  • DOI: https://doi.org/10.1007/s002200050376

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