{"paper":{"title":"A note on 2D focusing many-boson systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Mathieu Lewin (CEREMADE), Nicolas Rougerie (LPMMC), Phan Th\\`anh Nam (IST Austria)","submitted_at":"2015-09-30T07:51:18Z","abstract_excerpt":"We consider a 2D quantum system of $N$ bosons in a trapping potential $|x|^s$, interacting via a pair potential of the form $N^{2\\beta-1} w(N^\\beta x)$. We show that for all $0 \\textless{} \\beta \\textless{} (s+1)/(s+2)$, the leading order behavior of ground states of the many-body system is described in the large $N$ limit by the corresponding cubic nonlinear Schr{\\\"o}dinger energy functional. Our result covers the focusing case ($w \\leq 0$) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X.~Chen and J.~Holmer for harmonic traps ($s=2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09045","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"}