Low-temperature relaxation in glassy systems

The stress-relaxation function σ(t) in a stabilized glass is described by a potential-barrier model which is based on separating geometric packing considerations from thermal excitations in the dynamical evolution of a many-body system. The analysis proceeds in stages: (1) The configuration space is uniquely divided into cells, each associated with a minimum on the potential energy φ hypersurface. (2) ‘‘Crystal-free’’ particle packings are isolated. (3) Since the φ hypersurface in the amorphous manifold is topographically rough over a wide range of length scales, a coarse graining is carried out to suppress small-scale roughness. (4) Stress relaxation is connected with transition between cells which involve localized particle motions. A master equation describes the time-dependent residence probabilities in the cells. The basic physical assumption is that the slowest structural rearrangements in a dense, highly viscous supercooled fluid occur on a molecular length scale via self-diffusion. We find that σ(t)=${\phi }_0$exp[-(t/τ${)}^{\alpha }$]; for t≪τ, α=(1/3); for t∼τ, α=(1/2); for t≫τ, α=1. The temperature dependence of τ is governed by the self-diffusion of the viscous fluid.