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

A statistical analysis of the geometries of particle trajectories in the supercooled liquid state is reported. We examine two structurally different fragile glass-forming liquids simulated by molecular dynamics. In both liquids, the trajectories are found to exhibit a long-range localisation distinct from the short-range localisation within the cage of nearest neighbours. This novel diffusion anomaly is interpreted as a result of the potential-energy landscape topography of fragile glass-formers where the local energy minima coalesce into metabasins - compact domains with low escape probability.