On the dynamics of Bose gases and Bose-Einstein condensates

Monday, October 31, 2016 - 11:30am - 12:20pm
Keller 3-180
Thomas Chen (The University of Texas at Austin)
The Hartree and the nonlinear Schrodinger equation can be derived as the mean field limit of the dynamics of an interacting gas of Bosons exhibiting Bose-Einstein condensation; the nonlinear dispersive PDE describes the dynamics of the Bose-Einstein condensate. The topic of this talk is an extension to the Hartree equation, which describes thermal fluctuations around the Bose-Einstein condensate. Using quasifree reduction, we derive the Hartree-Fock-Bogoliubov (HFB) equations, and discuss the well-posedness of the corresponding Cauchy problem. In particular, the emergence of Bose-Einstein condensates at positive temperature via a self-consistent Gibbs state is addressed. This is based on joint work with V. Bach, S. Breteaux, J. Froehlich, and I.M. Sigal.
MSC Code: 
35Q55, 81V70