{"paper":{"title":"On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Robert Seiringer, Yujin Guo","submitted_at":"2013-01-24T01:02:50Z","abstract_excerpt":"We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength $a$ satisfies $a < a^*= \\|Q\\|_2^2$, where $Q$ is the unique positive radial solution of $\\Delta u-u+u^3=0$ in $\\R^2$. We present a detailed analysis of the behavior of minimizers as $a$ approaches $a^*$, where all the mass concentrates at a global minimum of the trapping potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5682","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"}