  We investigate the time evolution of correlations in the Bose-Hubbard model
following a quench from the superfluid to the Mott insulating phase. For large
values of the final interaction strength the system approaches a distinctly
non-equilibrium steady state that bears strong memory of the initial
conditions. In contrast, when the final interaction strength is comparable to
the hopping, the correlations are rather well approximated by those at thermal
equilibrium. The existence of two distinct non-equilibrium regimes is
surprising given the non-integrability of the Bose-Hubbard model. We relate
this phenomena to the role of quasi-particle interactions in the Mott
insulating state.
