  We experimentally and numerically investigate the expansion of initially
localized ultracold bosons in homogeneous one- and two-dimensional optical
lattices. We find that both dimensionality and interaction strength crucially
influence these non-equilibrium dynamics. While the atoms expand ballistically
in all integrable limits, deviations from these limits dramatically suppress
the expansion and lead to the appearance of almost bimodal cloud shapes,
indicating diffusive dynamics in the center surrounded by ballistic wings. For
strongly interacting bosons, we observe a dimensional crossover of the dynamics
from ballistic in the one-dimensional hard-core case to diffusive in two
dimensions, as well as a similar crossover when higher occupancies are
introduced into the system.
