  The quantum dynamics of colliding Bose-Einstein condensates with 150 000
atoms are simulated directly from the Hamiltonian using the stochastic
positive-P method. Two-body correlations between the scattered atoms and their
velocity distribution are found for experimentally accessible parameters.
Hanbury Brown-Twiss or thermal-like correlations are seen for copropagating
atoms, while number correlations for counterpropagating atoms are even stronger
than thermal correlations at short times. The coherent phase grains grow in
size as the collision progresses with the onset of growth coinciding with the
beginning of stimulated scattering. The method is versatile and usable for a
range of cold atom systems.
