{"paper":{"title":"Spectral Gaps of Almost Mathieu 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":"2013-11-04T12:00:07Z","abstract_excerpt":"For almost Mathieu operator $(H_{\\lambda,\\alpha,\\theta}u)_n=u_{n+1}+u_{n-1}+2\\lambda \\cos2\\pi(\\theta+n\\alpha)u_n$, the dry version of Ten Martini problem predicts that the spectrum $\\Sigma_{\\lambda,\\alpha}$ of $ H_{\\lambda,\\alpha,\\theta}$ has all gaps open for all $\\lambda\\neq 0$ and $ \\alpha \\in \\mathbb{R}\\backslash \\mathbb{Q}$.\n  Avila and Jitomirskaya prove that $\\Sigma_{\\lambda,\\alpha}$ has all gaps open for Diophantine $\\alpha$ and $0<|\\lambda|<1$.\n  In the present paper, we show that $\\Sigma_{\\lambda,\\alpha}$ has all gaps open for all $ \\alpha \\in \\mathbb{R}\\backslash \\mathbb{Q}$ with sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0658","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"}