Thomas Chen (UT Austin)

Title: Derivation of NLS from interacting Bose gases/Fluctuation dynamics around Bose-Einstein condensates

In the first talk, we discuss the mean field limit of a system of N interacting bosons in  Gross-Pitaevskii (BP) scaling. We explain how the nonlinear Schrodinger equation or Hartree equation is derived via the associated BBGKY hierarchy and the GP hierarchy equations as N tends to infinity, and how the NLS linked to the dynamics of Bose-Einstein condensates.  In particular, the proof of uniqueness of solutions to the GP hierarchy via the quantum de Finetti theorems is discussed. This is based on joint work with N. Pavlovic, C. Hainzl, and R. Seiringer.

In this second talk, we discuss 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.