{"paper":{"title":"The semi-classical scattering matrix from the point of view of Gaussian states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Maxime Ingremeau","submitted_at":"2016-12-20T17:52:50Z","abstract_excerpt":"In this note, we will consider semiclassical scattering for compactly supported non-trapping perturbations of the Laplacian on $\\mathbb{R}^d$. We will define a family of Gaussian states on $\\mathbb{S}^{d-1}$, parametrized by points in $T^*\\mathbb{S}^{d-1}$, and show that the action of the scattering matrix on a Gaussian state of parameter $\\rho\\in T^*\\mathbb{S}^{d-1}$ is still a Gaussian state, with parameter $\\kappa(\\rho)$, where $\\kappa$ is the (classical) scattering map. This is one way of saying that \\emph{the scattering matrix quantizes the scattering map}, complementary to a previous res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06783","kind":"arxiv","version":3},"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"}