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Quantum dynamical
bounds for ergodic potentials with underlying dynamics of
zero topological entropy
Rui Han and Svetlana Jitomirskaya |
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Vol. 12 (2019), No. 4, 867–902
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DOI: 10.2140/apde.2019.12.867
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Abstract |
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We show that positive Lyapunov exponents imply upper quantum dynamical bounds for Schrödinger operators , where is a piecewise Hölder function on a compact Riemannian manifold , and is a uniquely ergodic volume-preserving map with zero topological entropy. As corollaries we also obtain localization-type statements for shifts and skew-shifts on higher-dimensional tori with arithmetic conditions on the parameters. These are the first localization-type results with precise arithmetic conditions for multifrequency quasiperiodic and skew-shift potentials. |
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Keywords
transport exponent, multifrequency quasiperiodic,
skew-shift
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Mathematical Subject Classification 2010
Primary: 47B36, 81Q10
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Milestones
Received: 6 December 2016
Revised: 30 May 2018
Accepted: 5 July 2018
Published: 20 October 2018
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Authors |
| Rui Han | |
| Department of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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| Svetlana Jitomirskaya | |
| Department of Mathematics University of California Irvine, CA United States |
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