{"paper":{"title":"Continuous quasiperiodic Schr\\\"odinger operators with Gordon type potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Wencai Liu","submitted_at":"2017-09-17T07:02:12Z","abstract_excerpt":"Let us concern the quasi-periodic Schr\\\"odinger operator in the continuous case, \\begin{equation*}\n  (Hy)(x)=-y^{\\prime\\prime}(x)+V(x,\\omega x)y(x), \\end{equation*} where $V:(\\R/\\Z)^2\\to \\R$ is piecewisely $\\gamma$-H\\\"older continuous with respect to the second variable. Let $L(E)$ be the Lyapunov exponent of $Hy=Ey$. Define $\\beta(\\omega)$ as \\begin{equation*}\n  \\beta(\\omega)= \\limsup_{k\\to \\infty}\\frac{-\\ln ||k\\omega||}{k}. \\end{equation*} We prove that $H$ admits no eigenvalue in regime $\\{E\\in\\R:L(E)<\\gamma\\beta(\\omega)\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05614","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"}