Out-of-equilibrium dynamics of the two component Bose-Hubbard model

Cold atoms in optical lattices can be used as quantum simulators to study the temporal evolution of quantum systems, which has lead to increasing interest in the out-of-equilibrium dynamics of multi-component bosons in optical lattices. We study the Bose-Hubbard model for two component bosons using a strong-coupling approach within the closed time path formalism. We develop an effective theory for the action of this problem and obtain equations of motion for the superfluid order parameter. We study these equations of motion in the low-frequency, long wavelength limit for various initial conditions.