{"paper":{"title":"Arithmetic Spectral Transitions for the Maryland Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Svetlana Jitomirskaya, Wencai Liu","submitted_at":"2016-11-30T07:12:22Z","abstract_excerpt":"We give a precise description of spectra of the Maryland model $ (h_{\\lambda,\\alpha,\\theta}u)_n=u_{n+1}+u_{n-1}+ \\lambda \\tan \\pi(\\theta+n\\alpha)u_n$ for all values of parameters. We introduce an arithmetically defined index $\\delta (\\alpha, \\theta)$ and show that for $\\alpha\\notin\\mathbb{Q},\\,$ $\\sigma_{sc}(h_{\\lambda,\\alpha,\\theta})=\\overline{\\{e:\\gamma_{\\lambda}(e) <\\delta (\\alpha, \\theta) \\}}$ and $\\sigma_{pp}(h_{\\lambda,\\alpha,\\theta})=\\{e:\\gamma_{\\lambda}(e) \\geq \\delta (\\alpha, \\theta) \\}$. Since $\\sigma_{ac}(h_{\\lambda,\\alpha,\\theta})=\\emptyset,\\;$ this gives complete description of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10027","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"}