Superadiabatic dynamical density functional study of Brownian hard-spheres in time-dependent external potentials

Superadiabatic dynamical density functional theory (superadiabatic-DDFT), a first-principles approach based on inhomogeneous two-body correlation functions, is employed to investigate the response of interacting Brownian particles to time-dependent external driving. Predictions for the superadiabatic dynamics of the one-body density are made directly from the underlying interparticle interactions without the need for either adjustable fit parameters or simulation input. The external potentials we investigate have been chosen to probe distinct aspects of structural relaxation in dense, strongly interacting liquid states. Nonequilibrium density profiles predicted by the superadiabatic theory are compared with those obtained from both adiabatic DDFT and event-driven Brownian dynamics simulation. Our findings show that superadiabatic-DDFT accurately predicts the time-evolution of the one-body density