Analysis & PDE
- Anal. PDE
- Volume 12, Number 4 (2019), 867-902.
Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy
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.
Anal. PDE, Volume 12, Number 4 (2019), 867-902.
Received: 6 December 2016
Revised: 30 May 2018
Accepted: 5 July 2018
First available in Project Euclid: 30 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Han, Rui; Jitomirskaya, Svetlana. Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy. Anal. PDE 12 (2019), no. 4, 867--902. doi:10.2140/apde.2019.12.867. https://projecteuclid.org/euclid.apde/1540864855