{"paper":{"title":"Correlations of occupation numbers in the canonical ensemble and application to BEC in a 1D harmonic trap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aur\\'elien Grabsch, Christophe Texier, Olivier Giraud","submitted_at":"2018-02-07T18:29:31Z","abstract_excerpt":"We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\\overline{n_1\\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\\times p$ determinants involving the (canonical) mean occupations $\\overline{n_1}$, ..., $\\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\\leq N$). We draw some connection with the theory of symmetric functions, and obtain an exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02555","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"}