@article{2745,
abstract = {We consider the dynamics of N boson systems interacting through a pair potential N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if u t solves the GP equation, then the family of k-particle density matrices [InlineMediaObject not available: see fulltext.] solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5, we prove that as N→∞ the limit points of the k-particle density matrices of Ψ N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of this hierarchy remains an open question.},
author = {Elgart, Alexander and László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
journal = {Archive for Rational Mechanics and Analysis},
number = {2},
pages = {265 -- 283},
publisher = {Springer},
title = {{Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons}},
doi = {10.1007/s00205-005-0388-z},
volume = {179},
year = {2006},
}