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Sharp arithmetic localization for quasiperiodic operators with monotone potentials

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arxiv 2407.00703 v1 pith:2GJ4KDH3 submitted 2024-06-30 math.SP math-phmath.MP

Svetlana Jitomirskaya , Ilya Kachkovskiy This is my paper · ORCID
classification math.SPmath-phmath.MP
keywords arithmeticlocalizationmonotoneoperatorspotentialsquasiperiodicsharpanti-lipschitz
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We prove the universality of sharp arithmetic localization for all one-dimensional quasiperiodic Schr\"odinger operators with anti-Lipschitz monotone potentials.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition

    math.SP 2025-01 accept novelty 8.0 of 10

    Packing and multifractal dimensions of almost Mathieu spectral measures have upper bounds that vanish at the arithmetic transition where ln lambda equals beta.

  2. Universality of Packing Dimension Estimates for Spectral Measures of Quasiperiodic Operators: Monotone Potentials

    math.SP 2025-02 conditional novelty 5.0 of 10

    For γ-monotone quasiperiodic potentials, the upper packing dimension of spectral measures is at most 2(1-L/β) when L<β, and is zero when L≥β.

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