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

Wednesday, February 24, 2010 - 2:00pm - 2:45pm
EE/CS 3-180
Natasa Pavlovic (The University of Texas at Austin)
Keywords: Gross-Pitaevskii hierarchy

Abstract: In this talk we will discuss joint work with Thomas Chen on the
dynamics of a boson gas with three-body interactions in dimensions d=1,2. We prove that in the limit as 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. For factorized initial data, the solutions of the GP hierarchy are shown to be determined by solutions of a quintic nonlinear Schrodinger equation.

Time permitting, we will briefly describe our new approach for studying
well-posedness of the Cauchy problem for focusing and defocusing GP
MSC Code: