Abstract
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.
Citation
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
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