From Quantum Many Body Systems to Nonlinear Dispersive PDE, and Back

Thursday, May 28, 2015 - 11:00am - 11:50am
Lind 305
Natasa Pavlovic (The University of Texas at Austin)
The derivation of nonlinear dispersive PDE, such as the nonlinear
Schr{o}dinger (NLS) or nonlinear Hartree equations, from many body quantum
dynamics is a central topic in mathematical physics, which has been approached
by many authors in a variety of ways. In particular, one way to derive NLS is
via the Gross-Pitaevskii (GP) hierarchy, which is a coupled system of linear
non-homogeneous PDE that describes the dynamics of a gas of infinitely many
interacting bosons, while at the same time retains some of the features of a
dispersive PDE.

In this talk we will discuss the process of going from a quantum many body
system of bosons to the NLS via the GP. Also we will look into what a nonlinear
PDE such as the NLS can teach us about the GP hierarchy and quantum many body

The talk is based on joint works with T. Chen, C. Hainzl, R. Seiringer and N.