{"paper":{"title":"Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Abel Klein, Christian Sadel","submitted_at":"2011-01-22T22:45:44Z","abstract_excerpt":"The Bethe Strip of width $m$ is the cartesian product $\\B\\times\\{1,...,m\\}$, where $\\B$ is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have \"extended states\" for small disorder. More precisely, we consider Anderson-like Hamiltonians $\\;H_\\lambda=\\frac12 \\Delta \\otimes 1 + 1 \\otimes A + \\lambda \\Vv$ on a Bethe strip with connectivity $K \\geq 2$, where $A$ is an $m\\times m$ symmetric matrix, $\\Vv$ is a random matrix potential, and $\\lambda$ is the disorder parameter. Given any closed interval $I\\subset (-\\sqrt{K}+a_{\\mathrm{max}},\\sqrt{K}+a_{\\mathrm{min}})$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4328","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"}