{"paper":{"title":"Distribution of Resonances in Scattering by Thin Barriers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Jeffrey Galkowski","submitted_at":"2014-04-14T19:33:13Z","abstract_excerpt":"We study high energy resonances for the operators $-\\Delta +\\delta_{\\partial\\Omega}\\otimes V$ and $-\\Delta+\\delta_{\\partial\\Omega}'\\otimes V\\partial_\\nu$ where $\\Omega$ is strictly convex with smooth boundary, $V:L^2(\\partial\\Omega)\\to L^2(\\partial\\Omega)$ may depend on frequency, and $\\delta_{\\partial\\Omega}$ is the surface measure on $\\partial\\Omega$. These operators are model Hamiltonians for quantum corrals and leaky quantum graphs. We give a quantum version of the Sabine Law from the study of acoustics for both the $\\delta$ and $\\delta'$ interactions. It characterizes the decay rates (ima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3709","kind":"arxiv","version":5},"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"}