{"paper":{"title":"Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin Schlein, Horng-Tzer Yau, Laszlo Erdos","submitted_at":"2008-02-26T19:11:50Z","abstract_excerpt":"Consider a system of $N$ bosons in three dimensions interacting via a repulsive short range pair potential $N^2V(N(x_i-x_j))$, where $\\bx=(x_1, >..., x_N)$ denotes the positions of the particles. Let $H_N$ denote the Hamiltonian of the system and let $\\psi_{N,t}$ be the solution to the Schr\\\"odinger equation. Suppose that the initial data $\\psi_{N,0}$ satisfies the energy condition \\[ < \\psi_{N,0}, H_N \\psi_{N,0} > \\leq C N >. \\] and that the one-particle density matrix converges to a projection as $N \\to \\infty$. Then, we prove that the $k$-particle density matrices of $\\psi_{N,t}$ factorize "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3877","kind":"arxiv","version":3},"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"}