A statistical analysis of the geometries of particle trajectories in the supercooled liquid state was reported. The analysis presented was based upon the statistics of the first-passage trajectory length. Two structurally different fragile glass-forming liquids, simulated by using molecular dynamics, were examined. In both liquids, the trajectories were found to exhibit three distinct diffusion regimes. A short-range confinement to the cage of nearest-neighbours was followed by a persistent diffusion regime. At a still larger spatial scale, the particle trajectories exhibited a novel diffusion anomaly. This was a long-range localization which was distinct from the short-range localization. This phenomenon could be explained in terms of the potential-energy landscape topography, with the local energy minima coalescing into metabasins: compact domains having a low escape probability. It was also demonstrated that the persistent diffusion regime could be linked to the exponential decay of the self-part of the van Hove correlation function.

Anomalous Diffusion in Supercooled Liquids - a Long-Range Localization in Particle Trajectories. T.Oppelstrup, M.Dzugutov: Journal of Chemical Physics, 2009, 131[4], 044510