{"paper":{"title":"Ground states for 3D dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tao Yang, Xiao Luo","submitted_at":"2020-11-02T08:10:43Z","abstract_excerpt":"We consider ground states of three-dimensional dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses, which can be described equivalently by positive $L^2$-constraint critical point of the Gross-Pitaevskii energy functional \\[E(u)\\!=\\!\\frac{1}{2}\\int_{{\\mathbb{R}^3}} {|\\nabla u|}^2dx+\\frac{\\lambda_{1}}{2}\\int_{{\\mathbb{R}^3}} {| u|}^4dx+\\frac{\\lambda_{2}}{2} \\int_{\\mathbb{R}^{3}}\\left(K \\star|u|^{2}\\right)|u|^{2} d x+\\frac{2\\lambda_{3}}{p}\\int_{{\\mathbb{R}^3}} {|u|}^{p}dx,\\] where $2<p<\\frac{10}{3}$, $\\lambda_{3}<0$, $\\star$ is the convolution, $ K(x) \\!=\\! \\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.00804","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.00804/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"}