Computer simulation and mode-coupling theory analysis of time-dependent diffusion in two dimensional Lennard-Jones fluids

Self-consistent mode-coupling theory (MCT) has been used to calculate the time-dependent diffusion coefficient, D(t), in dense, two dimensional Lennard-Jones liquid, using detailed two particle pair and direct correlation functions. The well-known t-1 behavior of the long time tail of velocity correlation function is found to be latent at higher densities due to the dominance of the microscopic term at short and intermediate times. The calculated values are in good agreement with simulated D(t). At finite times, D(t) is found to exhibit interesting dependence on the density and the size of the system. Time-dependent diffusion can be used to discuss diffusion limited reactions in terms of D(t), with consequences which, however, are vastly different from those obtained with time independent diffusion coefficient