Sharp palindromic criterion for semi-uniform dynamical localization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909370385694720 |
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| author | Jitomirskaya, Svetlana Liu, Wencai Mi, Lufang |
| author_facet | Jitomirskaya, Svetlana Liu, Wencai Mi, Lufang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_21700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp palindromic criterion for semi-uniform dynamical localization Jitomirskaya, Svetlana Liu, Wencai Mi, Lufang Mathematical Physics Spectral Theory 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. |
| title | Sharp palindromic criterion for semi-uniform dynamical localization |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2410.21700 |