{"paper":{"title":"Natural Orbitals and Occupation Numbers for Harmonium: Fermions vs. Bosons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Christian Schilling","submitted_at":"2013-07-25T20:00:02Z","abstract_excerpt":"For a quantum system of N identical, harmonically interacting particles in a one-dimensional harmonic trap we calculate for the bosonic and fermionic ground state the corresponding 1-particle reduced density operator $\\rho_1$ analytically. In case of bosons $\\rho_1$ is a Gibbs state for an effective harmonic oscillator. Hence the natural orbitals are Hermite functions and their occupation numbers obey a Boltzmann distribution. Intriguingly, for fermions with not too large couplings the natural orbitals coincide up to just a very small error with the bosonic ones. In case of strong coupling thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6858","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"}