{"paper":{"title":"Metal-insulator transition for the almost Mathieu operator","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Svetlana Ya. Jitomirskaya","submitted_at":"1999-11-01T00:00:00Z","abstract_excerpt":"We prove that for Diophantine \\om and almost every \\th, the almost Mathieu operator, (H_{\\omega,\\lambda,\\theta}\\Psi)(n)=\\Psi(n+1) + \\Psi(n-1) + \\lambda\\cos 2\\pi(\\omega n +\\theta)\\Psi(n), exhibits localization for \\lambda > 2 and purely absolutely continuous spectrum for \\lambda < 2. This completes the proof of (a correct version of) the Aubry-Andr\\'e conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911265","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"}