{"paper":{"title":"The spectra of surface Maryland model for all phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Wencai Liu","submitted_at":"2016-11-30T07:23:19Z","abstract_excerpt":"We study the discrete Schr\\\"{o}dinger operators $H_{\\lambda,\\alpha,\\theta}$ on $\\ell^2(\\mathbb{Z}^{d+1})$ with surface potential of the form $V(n,x)=\\lambda \\delta(x)\\tan\\pi(\\alpha\\cdot n+\\theta)$, and $H_{\\lambda,\\alpha,\\theta}^{+}$ on $\\ell^2(\\mathbb{Z}^{d}\\times \\mathbb{Z}_+)$ with the boundary condition $ \\psi_{(n,-1)}=\\lambda \\tan\\pi(\\alpha\\cdot n+\\theta)\\psi_{(n,0)} $, where $\\alpha\\in \\mathbb{R}^d$ is rationally independent. We show that the spectra of $H_{\\lambda,\\alpha,\\theta}$ and $H_{\\lambda,\\alpha,\\theta}^{+}$ are $(-\\infty,\\infty)$ for all parameters. We can also determine the abs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10030","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"}