Excitations Are Localized and Relaxation Is Hierarchical in Glass-Forming Liquids

For several atomistic models of glass formers, at conditions below their glassy-dynamics-onset temperatures, T-o, we use importance sampling of trajectory space to study the structure, statistics, and dynamics of excitations responsible for structural relaxation. Excitations are detected in terms of persistent particle displacements of length a. At supercooled conditions, for a of the order of or smaller than a particle diameter, we find that excitations are associated with correlated particle motions that are sparse and localized, occupying a volume with an average radius that is temperature-independent and no larger than a few particle diameters. We show that the statistics and dynamics of these excitations are facilitated and hierarchical. Excitation-energy scales grow logarithmically with a. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. This nature of dynamics becomes increasingly dominant as temperature T is lowered. We show that slowing of dynamics upon decreasing temperature below T-o is the result of a decreasing concentration of excitations and concomitantly growing length scales for dynamical correlations that develop in a hierarchical manner, and further that the structural-relaxation time tau follows the parabolic law, log(tau/tau(o)) = J(2)(1/T - 1/T-o)(2), for T < T-o, where J, tau(o) and T-o can be predicted quantitatively from dynamics at short time scales. Particle motion is facilitated and directional, and we show that this becomes more apparent with decreasing T. We show that stringlike motion is a natural consequence of facilitated, hierarchical dynamics.