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2019 Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy
Rui Han, Svetlana Jitomirskaya
Anal. PDE 12(4): 867-902 (2019). DOI: 10.2140/apde.2019.12.867

Abstract

We show that positive Lyapunov exponents imply upper quantum dynamical bounds for Schrödinger operators H f , θ u ( n ) = u ( n + 1 ) + u ( n 1 ) + ϕ ( f n θ ) u ( n ) , where ϕ : is a piecewise Hölder function on a compact Riemannian manifold , and f : 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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Rui Han. Svetlana Jitomirskaya. "Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy." Anal. PDE 12 (4) 867 - 902, 2019. https://doi.org/10.2140/apde.2019.12.867

Information

Received: 6 December 2016; Revised: 30 May 2018; Accepted: 5 July 2018; Published: 2019
First available in Project Euclid: 30 October 2018

zbMATH: 06991221
MathSciNet: MR3869380
Digital Object Identifier: 10.2140/apde.2019.12.867

Subjects:
Primary: 47B36, 81Q10

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2019
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