Sharp localization on the first supercritical stratum for Liouville frequencies
Spectral Theory
2024-05-14 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We establish Anderson localization for Schr\"odinger operators with even analytic potentials on the first supercritical stratum for Liouville frequencies in the sharp regime , with being Avila's acceleration. This paper builds on the large deviation measure estimate and complexity bound scheme, originally developed for Diophantine frequencies by Bourgain, Goldstein and Schlag \cites{BG,BGS1,BGS2}, and the improved complexity bounds in \cite{HS1}. Additionally, it strengthens the large deviation estimates for weak Liouville frequencies in \cite{HZ}. We also introduce new ideas to handle Liouville frequencies in a sharp way.
Keywords
Cite
@article{arxiv.2405.07810,
title = {Sharp localization on the first supercritical stratum for Liouville frequencies},
author = {Rui Han},
journal= {arXiv preprint arXiv:2405.07810},
year = {2024}
}