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.
