Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length ? growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law ?(t) proportional to t(a), with a similar or equal to 1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a universal evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Automated summary

Recent works reveal that glass-forming liquids exhibit Fickian non-Gaussian diffusion, with non-Gaussian displacement distributions persisting even after attaining linearity in mean square displacement. These non-Gaussian deviations exhibit exponential tails with a growing decay length proportional to a power-law in time. The study examines data from different glass-forming systems and identifies a scaling law for the decay length, which holds for all systems regardless of dimensionality. Additionally, a universal characteristic time for the disappearance of exponential tails and the recovery of Gaussianity is found across different temperatures/concentrations within each system, related to the onset of Fickianity through a power-law.