Direct Observation of Stretched-Exponential Relaxation in Low-Temperature Lennard-Jones Systems Using the Cage Correlation Function

We report on the direct observation of stretched exponential relaxation in low-temperature monatomic Lennard-Jones systems which were cooled slowly from the liquid phase to form crystals with a large number of defects. We use the cage correlation function [E. Rabani, J. D. Gezelter, and B. J. Berne, J. Chem. Phys. 107, 6867 (1997)] which measures changes in atomic surroundings to observe the stretched exponential relaxations. We obtain a distribution of hopping rates assuming that the origin of the Kohlrausch-Williams-Watts law is from static disorder in the distribution of barrier heights.