{"paper":{"title":"Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasiperiodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fan Yang, Shiwen Zhang","submitted_at":"2018-04-28T03:45:16Z","abstract_excerpt":"We proved that Schr\\\"odinger operators with unbounded potentials $(H_{\\alpha,\\theta}u)_n=u_{n+1}+u_{n-1}+ \\frac{g(\\theta+n\\alpha)}{f(\\theta+n\\alpha)} u_n$ have purely singular continuous spectrum on the set $\\{E: 0<L(E)<\\delta{(\\alpha,\\theta;f,g)}\\}$, where $\\delta$ is an explicit function and $L$ is the Lyapunov exponent. We only require $f,g$ are H\\\"older continuous functions and $f$ has finitely many zeros with weak non-degenerate assumptions. Moreover, we show that for generic $\\alpha$ and a.e. $\\theta$, the spectral measure of $H_{\\alpha,\\theta}$ has full spectral/packing dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10732","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"}