{"paper":{"title":"Ground-state energy of one-dimensional free Fermi gases in the thermodynamic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Peter Otte, Wolfgang Spitzer","submitted_at":"2017-12-30T16:02:33Z","abstract_excerpt":"We study the ground-state energy of one-dimensional, non-interacting fermions subject to an external potential in the thermodynamic limit. To this end, we fix some (Fermi) energy $\\nu>0$, confine fermions with total energy below $\\nu$ inside the interval $[-L,L]$ and study the shift of the ground-state energy due to the potential $V$ in the thermodynamic limit $L\\to\\infty$. We show that the difference $\\mathcal{E}_L(\\nu)$ of the two ground-state energies with and without potential can be decomposed into a term of order one (leading to the Fumi-term) and a term of order $1/L$, which yields the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00144","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"}