  We explore how correlations evolve in a gas of lattice bosons when the
lattice depth is rapidly reduced. We find a simple closed form expression for
the static structure factor in the limit of vanishing interactions. The
corresponding real-space density correlation function shows multiple spatial
oscillations which linearly disperse as a function of time. By perturbatively
including the effects of the interactions we calculate how the boson
quasi-momentum evolves following the quench.
