From elementary steps to structural relaxation: a continuous-time random-walk analysis of a supercooled liquid.

We show that the dynamics of supercooled liquids, analyzed from computer simulations of the binary mixture Lennard-Jones system, can be described in terms of a continuous-time random walk (CTRW). The required discretization comes from mapping the dynamics on transitions between metabasins. This yields a quantitative link between the elementary step and the full structural relaxation. The analysis involves a verification of the CTRW conditions as well as a quantitative test of the predictions. The wave-vector dependence of the relaxation time and the degree of nonexponentiality can be expressed in terms of the first moments of the waiting time distribution.