{"paper":{"title":"Central spectral gaps of the almost Mathieu operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"I. Krasovsky","submitted_at":"2016-02-27T18:43:40Z","abstract_excerpt":"We consider the spectrum of the almost Mathieu operator $H_\\alpha$ with frequency $\\alpha$ and in the case of the critical coupling. Let an irrational $\\alpha$ be such that $|\\alpha-p_n/q_n|<c q_n^{-\\varkappa}$, where $p_n/q_n$, $n=1,2,\\dots$ are the convergents to $\\alpha$, and $c$, $\\varkappa$ are positive absolute constants, $\\varkappa<56$. Assuming certain conditions on the parity of the coefficients of the continued fraction of $\\alpha$, we show that the central gaps of $H_{p_n/q_n}$, $n=1,2,\\dots$, are inherited as spectral gaps of $H_\\alpha$ of length at least $c'q_n^{-\\varkappa/2}$, $c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08624","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"}