  We investigate the non-equilibrium dynamics of the bosonic Hubbard model
starting from inhomogeneous superfluid or Mott insulator initial states using
the truncated Wigner approximation (TWA). We find that the relaxation of the
system develops in two steps for sufficiently large interaction strengths:
after a fast relaxation the system gets caught in metastable prethermalized
states that precede the true equilibrium state. We find that the lifetime of
these prethermalized states increases by several orders of magnitude as we
increase the on-site interaction strength beyond a threshold value. We show
that the emergence of long-lived metastable states in the quantum dynamics is
associated with an ergodic (active) to non-ergodic (inactive) dynamical phase
transition in the ensemble of classical trajectories that contribute to the
semiclassical limit. This dynamic phase transition, which is very similar to
that found in different classical models of glasses, is closely related to the
dynamic heterogeneity of the classical relaxation.
