Thomas Chen and Natasa Pavlovic
The quintic NLS as the mean field limit of a Boson gas with three-body interactions
(375K, AMS Latex)
ABSTRACT. We investigate the dynamics of a boson gas with three-body interactions in dimensions d=1,2. We prove that in the limit where the particle number N tends to infinity, the BBGKY hierarchy of k-particle marginals converges to a limiting (Gross-Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness of solutions. The solutions of the GP hierarchy are shown to be determined by solutions of a quintic nonlinear Schrodinger equation. Our proof is based on, and extends, methods of Erdos-Schlein-Yau, Klainerman-Machedon, and Kirkpatrick-Schlein-Staffilani.