Title

Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy

Document Type

Article

Publication Date

1-1-2018

Abstract

We show that positive Lyapunov exponents imply upper quantum dynamical bounds for Schrödinger operators Hf,θ u(n) = u(n+1) + u(n-1) + ϕ (fnθ)u(n), where ϕ: M → ℝ is a piecewise Hölder function on a compact Riemannian manifold M, and f: M→M 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.

Publication Source (Journal or Book title)

Analysis and PDE

First Page

867

Last Page

892

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