Quantum dynamical bounds for long-range operators with skew-shift potentials
Wencai Liu, Matthew Powell, Xueyin Wang
TL;DR
This paper improves quantum dynamical bounds for long-range operators with skew-shift potentials by applying Weyl's and Vinogradov's methods to analyze skew-shift dynamics on semi-algebraic sets.
Contribution
It introduces a novel combination of Weyl's and Vinogradov's methods to enhance bounds for skew-shift operators, advancing previous results.
Findings
Improved quantum dynamical upper bounds for skew-shift operators.
Application of Weyl's and Vinogradov's methods to semi-algebraic sets.
Enhanced understanding of long-range operator dynamics.
Abstract
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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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Quantum Mechanics and Non-Hermitian Physics