  We study a quantum quench in the Bose-Hubbard model where the tunneling rate
$J$ is suddenly switched from zero to a finite value in the Mott regime. In
order to solve the many-body quantum dynamics far from equlibrium, we consider
the reduced density matrices for a finite number (one, two, three, etc.) of
lattice sites and split them up into on-site density operators, i.e., the mean
field, plus two-point and three-point correlations etc. Neglecting three-point
and higher correlations, we are able to numerically simulate the time-evolution
of the few-site density matrices and the two-point quantum correlations (e.g.,
their effective light-cone structure) for a comparably large number ${\cal
O}(10^3)$ of lattice sites.
