Transient Response of Disordered Systems to an Interaction Quench

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean field theory (DMFT) and coherent potential approximation (CPA) methods to the nonequilibrium many-body formalism using the Kadanoff-Baym-Keldysh complex time contour. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to an interaction quench of the isolated disordered system. Here, the interaction is abruptly changed from zero (non-interacting system) to another constant (finite) value at which it is subsequently kept. We observe via the time-dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of the final interaction strength. The real-time approach has the potential to shed new light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.