{"paper":{"title":"Equidistribution of phase shifts in semiclassical potential scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Andrew Hassell, Jesse Gell-Redman, Steve Zelditch","submitted_at":"2013-11-11T04:49:29Z","abstract_excerpt":"Consider a semiclassical Hamiltonian $H := h^{2} \\Delta + V - E$ where $\\Delta$ is the positive Laplacian on $\\mathbb{R}^{d}$, $V \\in C^{\\infty}_{0}(\\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that under an appropriate dynamical hypothesis on the Hamilton flow corresponding to $H$, the eigenvalues of the scattering matrix $S_{h}(V)$ define a measure on $\\mathbb{S}^{1}$ that converges to Lebesgue measure away from $1 \\in \\mathbb{S}^{1}$ as $h \\to 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2353","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"}