{"paper":{"title":"Ground state energy of the $\\delta$-Bose and Fermi gas at weak coupling from double extrapolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Sylvain Prolhac","submitted_at":"2016-10-12T13:51:22Z","abstract_excerpt":"We consider the ground state energy of the Lieb-Liniger gas with $\\delta$ interaction in the weak coupling regime $\\gamma\\to0$. For bosons with repulsive interaction, previous studies gave the expansion $e_{\\text{B}}(\\gamma)\\simeq\\gamma-4\\gamma^{3/2}/3\\pi+(1/6-1/\\pi^{2})\\gamma^{2}$. Using a numerical solution of the Lieb-Liniger integral equation discretized with $M$ points and finite strength $\\gamma$ of the interaction, we obtain very accurate numerics for the next orders after extrapolation on $M$ and $\\gamma$. The coefficient of $\\gamma^{5/2}$ in the expansion is found approximately equal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08912","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"}