Two distinct time scales in the dynamics of a dense hard-sphere liquid

The dynamic behavior of a dense hard-sphere liquid is studied by numerically integrating a set of Langevin equations that incorporate a free energy functional of the Ramakrishnan-Yussouff form. At relatively low densities, the system remains, during the time scale of our simulation, in the neighborhood of the metastable local minimum of the free energy that represents a uniform liquid. At higher densities, the system is found to fluctuate near the uniform liquid minimum for a characteristic period of time before making a transition to an inhomogeneous minimum of the free energy. The time that the system spends in the vicinity of the liquid minimum before making a transition to another one defines a new time scale of the dynamics. This time scale is found to decrease sharply as the density is increased above a characteristic value. Implications of these observations on the interpretation of experimental and numerical data on the dynamics of supercooled liquids are discussed.