Vol. 12, No. 4, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 8, 1891–2146
Issue 7, 1643–1890
Issue 7, 1397–1644
Issue 6, 1397–1642
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy

Rui Han and Svetlana Jitomirskaya

Vol. 12 (2019), No. 4, 867–902
DOI: 10.2140/apde.2019.12.867
Abstract

We show that positive Lyapunov exponents imply upper quantum dynamical bounds for Schrödinger operators Hf,θu(n) = u(n + 1) + u(n 1) + ϕ(fnθ)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.

Keywords
transport exponent, multifrequency quasiperiodic, skew-shift
Mathematical Subject Classification 2010
Primary: 47B36, 81Q10
Milestones
Received: 6 December 2016
Revised: 30 May 2018
Accepted: 5 July 2018
Published: 20 October 2018
Authors
Rui Han
Department of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Svetlana Jitomirskaya
Department of Mathematics
University of California
Irvine, CA
United States