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

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

2008-12-15

arxiv.org/abs/0812.2740v2

Journal of Functional Analysis, 260 (4), 959 - 997, 2011

Physics

Mathematical Physics

AMS Latex, 35 pages

Scientific paper

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 Schr\"odinger equation. Our proof is based on, and extends, methods of Erd\"os-Schlein-Yau, Klainerman-Machedon, and Kirkpatrick-Schlein-Staffilani.

Affiliated with

Also associated with

No associations

Rating

The quintic NLS as the mean field limit of a Boson gas with three-body interactions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The quintic NLS as the mean field limit of a Boson gas with three-body interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The quintic NLS as the mean field limit of a Boson gas with three-body interactions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-348735