Mean-squared displacement of a molecule moving in a glassy system - art. no. 011503

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell mole cule consisting of two fused hard spheres immersed in a dense hard-sphere s ystem is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone funct ion for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the cy process, which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The ru process for molecule s with a large elongation is shown to exhibit an anomalously wide crossover interval between the end of the von Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary nonm onotonically as a function of its elongation.