Fickian non-Gaussian diffusion in glass-forming liquids

Fickian yet non-Gaussian Diffusion (FnGD), a most intriguing open issue in soft matter, is generically associated to some dynamical and/or structural heterogeneity of the environment. Here we investigate the features of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple model of molecular liquid. We demonstrate that FnGD strengthens on approaching the glass transition, by identifying distinct time-scales for Fickianity, τF , and for restoring of Gaussianity, τG > τF , as well as their associated length-scales, ξF and ξG. We find τG ∝ τ γ F with γ ≃ 1.8 for both systems. In the deep FnGD regime, the displacement distributions display exponential tails.We show that, in simulations, the time-dependent decay lengths l(t) at different temperatures all collapse onto a power-law master-curve l(t) ξG∝ ( tτG)α, with α = 0.33. A similar collapse, if less sharp, is also found in experiments, seemingly with the same exponent α. We further discuss the connections of the time- and length-scales characterizing FnGD with structural relaxation and dynamic heterogeneity.