{"paper":{"title":"Correlation energy of anisotropic quantum dots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","cond-mat.str-el","physics.comp-ph"],"primary_cat":"physics.chem-ph","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos, Yan Zhao","submitted_at":"2011-08-01T08:15:34Z","abstract_excerpt":"We study the $D$-dimensional high-density correlation energy $\\Ec$ of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the behavior of $\\Ec$ as a function of the anisotropy $\\alpha^{-1}$. In particular, we are interested in the limit where the anisotropy goes to infinity ($\\alpha\\to0$) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of $\\alpha$ from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0257","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"}