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Quantum dynamical bounds for long-range operators with skew-shift potentials

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arxiv 2411.00176 v1 pith:FEULTCIV submitted 2024-10-31 math-ph math.MPmath.NTmath.SP

Wencai Liu , Matthew Powell , Xueyin Wang This is my paper · ORCID
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keywords skew-shiftboundsdynamicallong-rangemethodoperatorspotentialsquantum
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We employ Weyl's method and Vinogradov's method to analyze skew-shift dynamics on semi-algebraic sets. Consequently, we improve the quantum dynamical upper bounds of Jitomirskaya-Powell, Liu, and Shamis-Sodin for long-range operators with skew-shift 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. The curious spectra and dynamics of non-locally finite crystals

    math.SP 2024-11 accept novelty 7.0 of 10

    Periodic graphs with infinitely many neighbours per vertex can have purely singular continuous spectrum, flat bands with only delocalized eigenvectors, and ballistic transport without dispersive estimates.

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