{"paper":{"title":"Ballistic Behavior for Random Schr\\\"odinger 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":"2011-06-08T23:55:29Z","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 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. Under certain conditions on $A$ and $K$, for which we previously proved the existence of absolutely continuous spectrum for small $\\lambda$, we now obtain ballistic behavior for the spreading of wave pack"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1689","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"}