Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons |
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| Authors: | Alexander Elgart László Erdős Benjamin Schlein Horng-Tzer Yau |
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| Affiliation: | (1) Department of Mathematics, Stanford University, Stanford, CA 94305, USA;(2) Institute of Mathematics, University of Munich, Theresienstr. 39, D-80333 Munich, Germany |
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| 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  | |
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