08-235 Thomas Chen and Natasa Pavlovic

The quintic NLS as the mean field limit of a Boson gas with three-body interactions (375K, AMS Latex) Dec 18, 08

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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.

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