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Continuity of the Measure of the Spectrum for Quasiperiodic Schrödinger Operators with Rough Potentials

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Abstract

We study discrete quasiperiodic Schrödinger operators on \({\ell^2(\mathbb{Z})}\) with potentials defined by γ-Hölder functions. We prove a general statement that for γ > 1/2 and under the condition of positive Lyapunov exponents, measure of the spectrum at irrational frequencies is the limit of measures of spectra of periodic approximants. An important ingredient in our analysis is a general result on uniformity of convergence from above in the subadditive ergodic theorem for strictly ergodic cocycles.

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Authors and Affiliations

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

    Svetlana Jitomirskaya

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

    Rajinder Mavi

Authors
  1. Svetlana Jitomirskaya
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  2. Rajinder Mavi
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Correspondence to Svetlana Jitomirskaya.

Additional information

Communicated by B. Simon

The work was supported by NSF Grant DMS-1101578.

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Jitomirskaya, S., Mavi, R. Continuity of the Measure of the Spectrum for Quasiperiodic Schrödinger Operators with Rough Potentials. Commun. Math. Phys. 325, 585–601 (2014). https://doi.org/10.1007/s00220-013-1856-1

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