Anomalous diffusion in supercooled liquids: a long-range localization in particle trajectories.

A statistical analysis of the geometries of particle trajectories in the supercooled liquid state is reported. The analysis we present here is based on the statistics of the first-passage trajectory length. We examine two structurally different fragile glass-forming liquids simulated by molecular dynamics. In both liquids, the trajectories are found to reveal three distinct diffusion regimes. A short-range confinement to the cage of nearest neighbors is followed by a persistent diffusion regime. At a still larger spatial scale, the particle trajectories demonstrate a novel diffusion anomaly: a long-range localization distinct from the short-range localization. This phenomenon can be interpreted in terms of the potential-energy landscape topography with the local energy minima coalescing into metabasins--compact domains with low escape probability. We also demonstrate that the persistent diffusion regime can be linked to the exponential decay of the self-part of the van Hove correlation function.