{"paper":{"title":"Correlation energy of the one-dimensional Coulomb gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.other","physics.chem-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos","submitted_at":"2012-07-04T06:13:15Z","abstract_excerpt":"We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where $r_s$ is the Seitz radius), we find that the reduced correlation energy is $\\Ec(r_s,n) = \\eps^{(2)}(n) + O(r_s)$, and we report explicit expressions for $\\eps^{(2)}(n)$. In the thermodynamic (large-$n$) limit of this, we show that $\\Ec(r_s) = - \\pi^2/360 + O(r_s)$. In the low-density (large-$r_s$) limit, the system forms a Wigner crystal and we find that $\\Ec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0908","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"}