Central limit theorem for Bose gases interacting through singular potentials

Abstract

We consider a system of $N$ bosons in the limit $N \rightarrow \infty$, interacting through singular potentials. For initial data exhibiting Bose-Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic non-linear Schr\"odinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.