Dynamic scaling for anomalous transport in supercooled liquids

The anomalous mesoscopic transport in supercooled liquids was investigated using three-dimensional molecular dynamics simulation. We show that the dynamic correlation length, ξ, can be identified as a crossover length between the microscopic and macroscopic transports. We also find that in highly supercooled states, where a clear stress plateau is observed in the stress autocorrelation, cooperative transport, in both the (longitudinal) density diffusion and the (transverse) viscous relaxation, can be characterized by the single length scale, ξ. The present identification of the dynamic correlation length has an advantage over other characterization methods in that it directly interprets the anomalous hydrodynamic transport in terms of the growing length scale. In the context of the present study, we provide a simple explanation for the long-standing problem of the breakdown of the Stokes-Einstein relation.