Sharp palindromic criterion for semi-uniform dynamical localization
Mathematical Physics
2024-10-30 v1 math.MP
Spectral Theory
Abstract
We develop a sharp palindromic argument for general 1D operators, that proves absence of semi-uniform localization in the regime of exponential symmetry-based resonances. This provides the first examples of operators with dynamical localization but no SULE/SUDL, as well as with nearly uniform distribution of centers of localization in absence of SULE. For the almost Mathieu operators, this also leads to a sharp arithmetic criterion for semi-uniformity of dynamical localization in the Diophantine case.
Cite
@article{arxiv.2410.21700,
title = {Sharp palindromic criterion for semi-uniform dynamical localization},
author = {Svetlana Jitomirskaya and Wencai Liu and Lufang Mi},
journal= {arXiv preprint arXiv:2410.21700},
year = {2024}
}