We study the quench from the Mott to the superfluid phase in the Bose-Hubbard
model and investigate the spatial-temporal growth of phase coherence, i.e.,
phase locking between initially uncorrelated sites. To this end, we establish a
hierarchy of correlations via a controlled expansion into inverse powers of the
coordination number 1/Z. It turns out that the off-diagonal long-range order
spreads with a constant propagation speed, forming local condensate patches,
whereas the phase correlator follows a diffusion-like growth rate.Comment: 4 page