Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation

We solved the mode-coupling equations for the Kob-Andersen binary mixture using the structure factors calculated from Brownian dynamics simulations of the same system. We found, as was previously observed, that the mode-coupling temperature, Tc, inferred from simulations is about two times greater than that predicted by the theory. However, we find that many time dependent quantities agree reasonably well with the predictions of the mode-coupling theory if they are compared at the same reduced temperature epsilon = (T-Tc)/Tc, and if epsilon is not too small. Specifically, the simulation results for the incoherent intermediate scattering function, the mean square displacement, the relaxation time and the self-diffusion coefficient agree reasonably well with the predictions of the mode-coupling theory. We find that there are substantial differences for the non-Gaussian parameter. At small reduced temperatures the probabilities of the logarithm of single particle displacements demonstrate that there is hopping-like motion present in the simulations, and this motion is not predicted by the mode-coupling theory. The wave vector dependent relaxation time is shown to be qualitatively different than the predictions of the mode-coupling theory for temperatures where hopping-like motion is present.