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 structure factors calculated from Brownian dynamics simulations of the same system. We found, as was previously observed, that the mode-coupling temperature T-c 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-T-c)/T-c, 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 from the predictions of the mode-coupling theory for temperatures where hopping-like motion is present.