{"paper":{"title":"Gaussian decay for a difference of traces of the Schr\\\"odinger semigroup associated to the isotropic harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Baptiste Savoie, Mathieu Beau (STP-DIAS)","submitted_at":"2014-01-27T19:46:25Z","abstract_excerpt":"This paper deals with the derivation of a sharp estimate on the difference of traces of the one-parameter Schr\\\"odinger semigroup associated to the quantum isotropic harmonic oscillator. Denoting by $H_{\\infty,\\kappa}$ the self-adjoint realization in $L^{2}(\\mathbb{R}^{d})$, $d \\in \\{1,2,3\\}$ of the Schr\\\"odinger operator $-\\frac{1}{2} \\Delta + \\frac{1}{2} \\kappa^{2}\\vert \\bold{x}\\vert^{2}$, $\\kappa>0$ and by $H_{L,\\kappa}$, $L>0$ the Dirichlet realization in $L^{2}(\\Lambda_{L}^{d})$ where $\\Lambda_{L}^{d}:=\\{\\bold{x} \\in \\mathbb{R}^{d}:- \\frac{L}{2} < x_{l} < \\frac{L}{2},\\,l=1,\\ldots,d\\}$, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6980","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"}