Cold atoms in optical lattices can realise the Bose Hubbard model which has a quantum phase transition between a superfluid phase and a Mott insulating phase that can be accessed by changing the depth of the optical lattice. The attractive feature of cold atoms is that parameters in the Hamiltonian be tuned in real time to cross the quantum critical point. I will discuss the real time dynamics of the Bose Hubbard model as formulated within the Schwinger-Keldysh technique. This allows for a treatment in which thermal effects and the effects of time dependent parameters can be described in both the superfluid and Mott insulating phases. By obtaining an appropriate real time effective action, I obtain dynamical equations for the superfluid order parameter as hopping is tuned so that the system crosses the superfluid phase boundary. Under a quench in the hopping, the system generically enters a metastable state whose properties depend on the timescale for the quench. These results will be related to recent experimental work
concerning equilibration of cold atoms after a quantum quench.