{"paper":{"title":"Long-lived Scattering Resonances and Bragg Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","physics.optics"],"primary_cat":"math.OC","authors_text":"Braxton Osting, Michael I. Weinstein","submitted_at":"2013-01-16T06:47:44Z","abstract_excerpt":"We consider a system governed by the wave equation with index of refraction $n(x)$, taken to be variable within a bounded region $\\Omega\\subset \\mathbb R^d$, and constant in $\\mathbb R^d \\setminus \\Omega$. The solution of the time-dependent wave equation with initial data, which is localized in $\\Omega$, spreads and decays with advancing time. This rate of decay can be measured (for $d=1,3$, and more generally, $d$ odd) in terms of the eigenvalues of the scattering resonance problem, a non-selfadjoint eigenvalue problem governing the time-harmonic solutions of the wave (Helmholtz) equation whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3600","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"}