Universality of liquid dynamics

We investigate the origin of the Stokes-Einstein relation in liquids. The hard-sphere dynamics is analyzed using a new measure of structural relaxation - the minimum Euclidean distance between configurations of particles. It is shown that the universal relation between the structural relaxation and diffusion in liquids is caused by the existence of one dominating length scale imposed by the structural correlations and associated with de Gennes narrowing. We demonstrate that this relation can be described by a model of independent random walkers under the single-occupancy constraint.