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Exact dynamical decay rate for the almost Mathieu operator

Jitomirskaya, Svetlana and Krüger, Helge and Liu, Wencai (2020) Exact dynamical decay rate for the almost Mathieu operator. Mathematical Research Letters, 27 (3). pp. 789-808. ISSN 1073-2780. https://resolver.caltech.edu/CaltechAUTHORS:20200918-101347800

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Abstract

We prove that the exponential decay rate in expectation is well defined and is equal to the Lyapunov exponent, for supercritical almost Mathieu operators with Diophantine frequencies.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.4310/mrl.2020.v27.n3.a8DOIArticle
https://arxiv.org/abs/1812.02860arXivDiscussion Paper
Additional Information:© 2020 by International Press of Boston, Inc. Received 6 December 2018; Accepted 8 June 2019. S.J. was supported by NSF DMS-1401204 and DMS-1901462. W. L. was supported by NSF DMS-1700314/2015683, DMS-2000345, the AMS-Simons Travel Grant 2016-2018 and the Southeastern Conference (SEC) Faculty Travel Grant 2020-2021. S.J. and W.L. are grateful to the Isaac Newton Institute for Mathematical Sciences, Cambridge, for its hospitality, supported by EPSRC Grant Number EP/K032208/1, during the 2015 programme Periodic and Ergodic Spectral Problems where an important progress on this work was made.
Funders:
Funding AgencyGrant Number
NSFDMS-1401204
NSFDMS-1901462
NSFDMS-1700314
NSFDMS-2015683
NSFDMS-2000345
American Mathematical Society2016-2018
Southeastern Conference (SEC) Faculty Travel Grant2020-2021
Engineering and Physical Sciences Research Council (EPSRC)EP/K032208/1
Issue or Number:3
Record Number:CaltechAUTHORS:20200918-101347800
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200918-101347800
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105446
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Sep 2020 17:56
Last Modified:18 Sep 2020 17:56

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