nonlinear Schr¨odinger equation

On the role of pair correlations in the evolution of Bose-Einstein condensates

Prof. Manoussos Grillakis, Department of Mathematics, University of Maryland in College Park.

Dec 7, 15:30 - 17:00

B1 L3 R3119

nonlinear Schr¨odinger equation

A Bose gas at zero temperature is described by a mean field which satisfies the cubic nonlinear Schr¨odinger equation (NLS) otherwise known as the Gross- Pitaevski equation. The mean field describes the evolution of the condensate in an average sense. I will describe a technique that introduces pair correlations in the evolution of the condensate. The resulting approximation tracks the evolu- tion of the condensate in norm provided that the pair wave-function satisfies an interesting system of coupled NLS equations. I will discuss the nonlinear struc- ture of the NLS system as well as a novel approach to the question of global existence of solutions of the system.