  The Balian-V\'en\'eroni (BV) variational principle, which optimizes the
evolution of the state according to the relevant observable in a given
variational space, is used at the mean-field level to determine the particle
number fluctuations in fragments of many-body systems. For fermions, the
numerical evaluation of such fluctuations requires the use of a time-dependent
Hartree-Fock (TDHF) code. Proton, neutron and total nucleon number fluctuations
in fragments produced in collisions of two 40Ca are computed for a large range
of angular momenta at a center of mass energy E_cm=128 MeV, well above the
fusion barrier. For deep-inelastic collisions, the fluctuations calculated from
the BV variational principle are much larger than standard TDHF results, and
closer to mass and charge experimental fluctuations. For the first time,
correlations between proton and neutron numbers are determined within a quantum
microscopic approach. These correlations are shown to be larger with exotic
systems where charge equilibration occurs.
