{"paper":{"title":"The second order Huang-Yang formula to the 3D Fermi gas: the Gross-Pitaevskii regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jiahao Wu, Xuwen Chen, Zhifei Zhang","submitted_at":"2024-10-22T02:08:48Z","abstract_excerpt":"For a system of $N$ Fermions of spin $1/2$, with its interaction potential of scattering length $a$, the classical Huang-Yang formula states that the energy density $e(\\rho)$ is of the form\n  \\begin{equation*}\n  e(\\rho)=\\frac{3}{5}(3\\pi^2)^{\\frac{2}{3}}\\rho^{\\frac{5}{3}}+2\\pi a\\rho^2\n  +\\frac{12}{35}(11-2\\ln2)3^{\\frac{1}{3}}\\pi^{\\frac{2}{3}}a^2\\rho^{\\frac{7}{3}}\n  +o(\\rho^{\\frac{7}{3}}).\n  \\end{equation*}\n  We consider a general system of $N$ Fermions of spin $1/\\mathbf{q}$ with the scattering length of the interaction potential at the scale $a\\propto N^{-1}$, that is, in the Gross-Pitaevskii "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16620","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.16620/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}