{"paper":{"title":"Absolutely Continuous Spectrum for the Quasi-periodic Schr\\\"{o}dinger Operator in Exponential Regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Wencai Liu, Xiaoping Yuan","submitted_at":"2013-11-04T13:01:44Z","abstract_excerpt":"Avila and Jitomirskaya prove that the quasi-periodic Schr\\\"{o}dinger operator $H_{\\lambda v,\\alpha,\\theta}$ has purely absolutely continuous spectrum for $\\alpha $ in sub-exponential regime (i.e., $\\beta(\\alpha)=0$) with small $\\lambda$, if $v$ is real analytic in a strip of real axis. In the present paper, we show that for all $\\alpha$ with $0<\\beta(\\alpha)<\\infty$, $H_{\\lambda v,\\alpha,\\theta}$ has purely absolutely continuous spectrum with small $\\lambda$, if $v$ is real analytic in strip $ |\\Im x|< C\\beta $, where $C$ is a large absolute constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0863","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"}