Dynamics of Highly Supercooled Liquids
  The diffusivity of tagged particles is demonstrated to be heterogeneous on time scales comparable to or less than the structural relaxation time %taking place at the interparticle distance in a highly supercooled liquid via 3D molecular dynamics simulation. The particle motions in the relatively active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Stokes-Einstein value. The van Hove self-correlation function $G_s(r,t)$ is shown to have a large $r$ tail which can be scaled in terms of $r/t^{1/2}$ for $t \ls 3 \tau_\alpha$, where $\tau_\alpha \cong$ the stress relaxation time. Its presence indicates heterogeneous diffusion in the active regions. However, the diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure ($\sim 3 \tau_{\alpha}$). 
Ryoichi Yamamoto and Akira Onuki