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arXiv · 2410.21700

Sharp palindromic criterion for semi-uniform dynamical localization

Svetlana Jitomirskaya·Wencai Liu·Lufang Mi
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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.

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Svetlana Jitomirskaya, Wencai Liu, Lufang Mi. 2024-10-29. Sharp palindromic criterion for semi-uniform dynamical localization. https://arxiv.org/abs/2410.21700

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