  We investigate the quantum many-body dynamics of dissociation of a
Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic
atoms and analyze the resulting atom-atom correlations. The quantum fields of
both the molecules and atoms are simulated from first principles in three
dimensions using the positive-P representation method. This allows us to
provide an exact treatment of the molecular field depletion and s-wave
scattering interactions between the particles, as well as to extend the
analysis to nonuniform systems. In the simplest uniform case, we find that the
major source of atom-atom decorrelation is atom-atom recombination which
produces molecules outside the initially occupied condensate mode. The unwanted
molecules are formed from dissociated atom pairs with non-opposite momenta. The
net effect of this process -- which becomes increasingly significant for
dissociation durations corresponding to more than about 40% conversion -- is to
reduce the atom-atom correlations. In addition, for nonuniform systems we find
that mode-mixing due to inhomogeneity can result in further degradation of the
correlation signal. We characterize the correlation strength via the degree of
squeezing of particle number-difference fluctuations in a certain
momentum-space volume and show that the correlation strength can be increased
if the signals are binned into larger counting volumes.
