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

28 Jul 2016  ·  Han Rui, Jitomirskaya Svetlana ·

In this paper we obtain upper quantum dynamical bounds as a corollary of positive Lyapunov exponent for Schr\"odinger operators $H_{f,\theta} u(n)=u(n+1)+u(n-1)+ \phi(f^n\theta)u(n)$, where $\phi : \mathcal{M}\to {\Bbb R}$ is a piecewise H\"older function on a compact Riemannian manifold $\mathcal{M}$, and $f:\mathcal{M}\to\mathcal{M}$ is a uniquely ergodic volume preserving map with zero topological entropy. As corollaries we 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 multi-frequency quasiperiodic and skew-shift potentials. read more

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Spectral Theory Mathematical Physics Mathematical Physics