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May 2018 Universal hierarchical structure of quasiperiodic eigenfunctions
Svetlana Jitomirskaya, Wencai Liu
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Ann. of Math. (2) 187(3): 721-776 (May 2018). DOI: 10.4007/annals.2018.187.3.3

Abstract

We determine exact exponential asymptotics of eigenfunctions and of corresponding transfer matrices of the almost Mathieu operators for all frequencies in the localization regime. This uncovers a universal structure in their behavior, governed by the continued fraction expansion of the frequency, explaining some predictions in physics literature. In addition it proves the arithmetic version of the frequency transition conjecture. Finally, it leads to an explicit description of several non-regularity phenomena in the corresponding non-uniformly hyperbolic cocycles, which is also of interest as both the first natural example of some of those phenomena and, more generally, the first non-artificial model where non-regularity can be explicitly studied.

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Svetlana Jitomirskaya. Wencai Liu. "Universal hierarchical structure of quasiperiodic eigenfunctions." Ann. of Math. (2) 187 (3) 721 - 776, May 2018. https://doi.org/10.4007/annals.2018.187.3.3

Information

Published: May 2018
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2018.187.3.3

Subjects:
Primary: 47B36
Secondary: 37C55 , 82B26

Keywords: Anderson localization , spectral transition , universal hierarchical structure

Rights: Copyright © 2018 Department of Mathematics, Princeton University

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Vol.187 • No. 3 • May 2018
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