{"paper":{"title":"On the Spectral and Propagation Properties of the Surface Maryland Model","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"F. Bentosela, L. Pastur, Ph. Briet","submitted_at":"2002-06-13T13:01:01Z","abstract_excerpt":"We study the discrete Schr\\\"odinger operator $H$ in $\\ZZ^d$ with the surface potential of the form $V(x)=g \\delta(x_1) \\tan \\pi(\\alpha \\cdot x_2+ \\omega)$, where for $x \\in \\ZZ^d$ we write $x=(x_1,x_2), \\quad x_1 \\in \\ZZ^{d_1}, x_2 \\in \\mathbb{Z}^{d_2}, \\alpha \\in \\R^{d_2}, \\omega \\in [0,1)$. We first consider the case where the components of the vector $\\alpha$ are rationally independent, i.e. the case of the quasi periodic potential. We prove that the spectrum of $H$ on the interval $[-d,d]$ (coinciding with the spectrum of the discrete Laplacian) is absolutely continuous. Then we show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0206019","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"}