{"paper":{"title":"Fluctuations of $N$-particle quantum dynamics around the nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin Schlein, Christian Brennecke, Marcin Napi\\'orkowski, Phan Th\\`anh Nam","submitted_at":"2017-10-26T15:01:26Z","abstract_excerpt":"We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3\\beta-1} V (N^\\beta x)$, for an arbitrary parameter $\\beta \\in (0,1)$. We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose-Einstein condensation in terms of a cubic nonlinear Schr\\\"odinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09743","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"}