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We study the real time dynamics of the Bose Hubbard model in the presence oftime-dependent hopping allowing for a finite temperature initial state. We usethe Schwinger-Keldysh technique to find the real-time strong coupling actionfor the problem at both zero and finite temperature. This action allows for thedescription of both the superfluid and Mott insulating phases. We use thisaction to obtain dynamical equations for the superfluid order parameter ashopping is tuned in real time so that the system crosses the superfluid phaseboundary. We find that under a quench in the hopping, the system genericallyenters a metastable state in which the superfluid order parameter has anoscillatory time dependence with a finite magnitude, but disappears whenaveraged over a period. We relate our results to recent cold atom experiments.

Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping