Packing and multifractal dimensions of almost Mathieu spectral measures have upper bounds that vanish at the arithmetic transition where ln lambda equals beta.
Quantum dynamical bounds for long-range operators with skew-shift potentials
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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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Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition
Packing and multifractal dimensions of almost Mathieu spectral measures have upper bounds that vanish at the arithmetic transition where ln lambda equals beta.