{"paper":{"title":"Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Rui Han, Svetlana Jitomirskaya","submitted_at":"2016-07-28T19:03:15Z","abstract_excerpt":"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-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08576","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}