From cage-jump motion to macroscopic diffusion in supercooled liquids

The evaluation of the long term stability of a material requires the estimation of its long-time dynamics. For amorphous materials such as structural glasses, it has proven difficult to predict the long-time dynamics starting from static measurements. Here we consider how long one needs to monitor the dynamics of a structural glass to predict its long–time features. We present a detailed characterization of the statistical features of the single-particle intermittent motion of structural glasses, and show that single–particle jumps are the irreversible events leading to the relaxation of the system. This allows to evaluate the diffusion constant on the time–scale of the jump duration, which is small and temperature independent, well before the system enters the diffusive regime. The prediction is obtained by analyzing the particle trajectories via a parameter-free algorithm.