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

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.

AMS Latex, 35 pages

References in corpus (4)

• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate
• Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics

Cited by in corpus (1)

• Global well-posedness for cubic NLS with nonlinear damping