Time scale for the onset of Fickian diffusion in supercooled liquids

We propose a quantitative measure of a time scale on which Fickian diffusion sets in for supercooled liquids, and we use Brownian dynamics computer simulations to determine the temperature dependence of this onset time in a Lennard-Jones binary mixture. The time for the onset of Fickian diffusion ranges between 6.5 and 31 times the relaxation time (the relaxation time is the characteristic relaxation time of the incoherent intermediate scattering function). The onset time increases faster with decreasing temperature than the relaxation time. Mean-squared displacement at the onset time increases with decreasing temperature.