Dynamic heterogeneities above and below the mode-coupling temperature. Evidence of a dynamic crossover

We examine dynamic heterogeneities in a model glass-forming fluid, a binary harmonic sphere mixture, above and below the mode-coupling temperature T_c. We calculate the ensemble independent susceptibility chi_4(tau_alpha) and the dynamic correlation length xi_4(tau_alpha) at the alpha-relaxation time tau_alpha. We also examine in detail the temperature dependence of tau_alpha and the diffusion coefficient D. For higher temperatures we find that the standard Stokes-Einstein relationship, D ~ tau_alpha^{-1}, holds, but at lower temperatures a fractional Stokes-Einstein relationship, D ~ tau_alpha^{-sigma} with sigma = 0.65, emerges. By examining the relationships between tau_alpha, D, chi_4(tau_alpha), and xi_4(tau_alpha) we determine that the emergence of the fractional Stokes-Einstein relationship is accompanied by a dynamic crossover from tau_alpha ~ e^{k_2 xi_4} at higher temperatures to tau_alpha ~ e^{k_1 xi_4^{3/2}} at lower temperatures.