The Quintic Nls as the Mean Field Limit of a Boson Gas with Three-body Interactions
نویسنده
چکیده
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 Schrödinger equation. Our proof is based on, and extends, methods of Erdös-Schlein-Yau, Klainerman-Machedon, and Kirkpatrick-Schlein-Staffilani.
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