{"paper":{"title":"Anderson localization for the completely resonant phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Wencai Liu, Xiaoping Yuan","submitted_at":"2013-11-04T12:42:02Z","abstract_excerpt":"For the almost Mathieu operator $ (H_{\\lambda,\\alpha,\\theta}u) (n)=u(n+1)+u(n-1)+ \\lambda v(\\theta+n\\alpha)u(n)$, Avila and Jitomirskaya guess that for every phase $ \\theta \\in \\mathscr{R} \\triangleq\\{\\theta\\in \\mathbb{R}\\;| \\; 2\\theta + \\alpha \\mathbb{Z} \\in \\mathbb{Z}\\}$, $H_{\\lambda,\\alpha,\\theta}$ satisfies Anderson localization if $ |\\lambda| > e^{ 2 \\beta}$. In the present paper, we show that for every phase $ \\theta \\in \\mathscr{R} $, $H_{\\lambda,\\alpha,\\theta}$ satisfies Anderson localization if $ |\\lambda| > e^{ 7 \\beta}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0862","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"}