JournalsjemsVol. 24, No. 5pp. 1723–1767

Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators

  • Svetlana Jitomirskaya

    University of California, Irvine, USA
  • Shiwen Zhang

    University of Minnesota, Minneapolis, USA
Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators cover
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Abstract

We introduce a notion of β\beta-almost periodicity and prove quantitative lower spectral/quantum dynamical bounds for general bounded β\beta-almost periodic potentials. Applications include the first sharp arithmetic spectral criterion for the entire family of supercritical analytic quasiperiodic Schrödinger operators and arithmetic spectral/quantum dynamical criteria for families with zero Lyapunov exponents, with applications to Sturmian potentials and the critical almost Mathieu operator. In particular, we disprove a 1994 conjecture of Wilkinson–Austin.

Cite this article

Svetlana Jitomirskaya, Shiwen Zhang, Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators. J. Eur. Math. Soc. 24 (2022), no. 5, pp. 1723–1767

DOI 10.4171/JEMS/1139