{"paper":{"title":"Asymptotic expressions for the hyperfine populations in the ground state of spin-1 condensates against a magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.atom-ph","authors_text":"C. G. Bao, Y. M. Liu, Y. Z. He","submitted_at":"2015-09-18T16:21:02Z","abstract_excerpt":"Based on the perturbation theory up to the second order, analytical asymptotic expressions for the variation of the population of hyperfine component $\\mu=0 $ particles in the ground state of spin-1 condensates against a magnetic field $B$ has been derived. The ranges of $B$ in which the asymptotic expressions are applicable have been clarified via a comparison of the numerical results from the analytical expressions and from a diagonalization of the Hamiltonian in a complete spin-space. It was found that, For $^{87}$Rb, the two analytical expressions, one for a weak and the other one for a st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05687","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"}