  We study the many body quantum evolution of bosonic systems in the mean field
limit. The dynamics is known to be well approximated by the Hartree equation.
So far, the available results have the form of a law of large numbers. In this
paper we go one step further and we show that the fluctuations around the
Hartree evolution satisfy a central limit theorem. Interestingly, the variance
of the limiting Gaussian distribution is determined by a time-dependent
Bogoliubov transformation describing the dynamics of initial coherent states in
a Fock space representation of the system.
