Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies
Published: Oct 29, 2025
Last Updated: Oct 29, 2025
Authors:Matthew Bradshaw, Titus de Jong, Wencai Liu, Audrey Wang, Xueyin Wang, Bingheng Yang
Abstract
We establish quantum dynamical upper bounds for quasi-periodic Schr\"odinger operators with Liouville frequencies. Our approach combines semi-algebraic discrepancy estimates for the Kronecker sequence $\{n\alpha\}$ with quantitative Green's function estimates adapted to the Liouville setting.