Dynamic heterogeneity and non-Gaussian behaviour in a model supercooled liquid

We use a recently derived reformulation of the diffusion constant (Stillinger and Debenedetti 2005 J. Phys. Chem. B 109 6604) to investigate heterogeneous dynamics and non-Gaussian diffusion in a binary Lennard-Jones mixture. Our work focuses on the joint probability distribution of particles with velocity v(0) at time t = 0 and eventual displacement Delta x at time t = Delta t. We show that this distribution attains a distinctive shape at the time of maximum non-Gaussian behaviour in the supercooled liquid. By performing a two-Gaussian fit of the displacement data, we obtain, in a non-arbitrary manner, two diffusive length scales inherent to the supercooled liquid and use them to identify spatially separated regions of mobile and immobile particles.