{"paper":{"title":"All couplings localization for quasiperiodic operators with Lipschitz monotone potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ilya Kachkovskiy, Svetlana Jitomirskaya","submitted_at":"2015-09-07T23:41:20Z","abstract_excerpt":"We establish Anderson localization for quasiperiodic operator families of the form\n  $$\n  (H(x)\\psi)(m)=\\psi(m+1)+\\psi(m-1)+\\lambda v(x+m\\alpha)\\psi(m)\n  $$ for all $\\lambda>0$ and all Diophantine $\\alpha$, provided that $v$ is a $1$-periodic function satisfying a Lipschitz monotonicity condition on $[0,1)$. The localization is uniform on any energy interval on which Lyapunov exponent is bounded from below."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02226","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"}