The quintic NLS as the mean field limit of a boson gas with three-body interactions

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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 of infinite particle number, the BBGKY hierarchy of k-particle marginals converges to a limiting (Gross-Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness of solutions. Factorized 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. © 2010 Elsevier Inc.

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Chen, T., & Pavlović, N. (2011). The quintic NLS as the mean field limit of a boson gas with three-body interactions. Journal of Functional Analysis, 260(4), 959–997. https://doi.org/10.1016/j.jfa.2010.11.003

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