In this talk, we shall discuss the non-equilibrium dynamics of the
Bose Hubbard model for both ramp periodic protocols using a projection
operator method which allows us to track the dynamics of the model
beyond mean-field theory. Our analysis shows that for periodic
dynamics, there exists special frequencies at which the system
wavefunction comes back to itself after a period. We connect to recent
experiments on these models using cold atoms and suggest further
experiments to test our theory. We also study the dynamics of these
bosons in the presence of an ``electric field'' in the Mott phase and
show that it provides an ideal test bed for Kibble-Zureck laws for
finite size systems.
