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, and show that single-particle jumps are the irreversible events leading to the relaxation of the system. This allows us to evaluate the diffusion constant on the time-scale of the jump duration, which is small and temperature independent, i.e. well before the system enters the diffusive regime. The prediction is obtained by analyzing the particle trajectories via a parameter-free algorithm.