{"paper":{"title":"Ballistic Transport and Absolute Continuity of One-Frequency Schr\\\"{o}dinger Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DS","authors_text":"Zhiyan Zhao, Zhiyuan Zhang","submitted_at":"2015-12-07T20:32:13Z","abstract_excerpt":"For the solution $u(t)$ to the discrete Schr\\\"odinger equation $${\\rm i}\\frac{d}{dt}u_n(t)=-(u_{n+1}(t)+u_{n-1}(t))+V(\\theta + n\\alpha)u_n(t), \\quad n\\in\\Z,$$ with $\\alpha\\in\\R\\setminus\\Q$ and $V\\in C^\\omega(\\T,\\R)$, we consider the growth rate with $t$ of its diffusion norm $\\langle u(t)\\rangle_{p}:=\\left(\\sum_{n\\in\\Z}(n^{p}+1) |u_n(t)|^2\\right)^\\frac12$, and the (non-averaged) transport exponents $$\\beta_u^{+}(p) := \\limsup_{t \\to \\infty} \\frac{2\\log \\langle u(t)\\rangle_{p}}{p\\log t}, \\quad \\beta_u^{-}(p):= \\liminf_{t \\to \\infty} \\frac{2\\log \\langle u(t)\\rangle_{p}}{p\\log t}.$$ We will show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02195","kind":"arxiv","version":2},"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"}