Cf. Vardeman et Jd. Gezelter, Comparing models for diffusion in supercooled liquids: The eutectic composition of the Ag-Cu alloy, J PHYS CH A, 105(12), 2001, pp. 2568-2574
We present a comparison between the Continuous Time Random Walk (CTRW) mode
l for dispersive transport and Zwanzig's model of self-diffusion in liquids
using the cage correlation function as a means for obtaining the character
istic hopping times. This comparison was done using a realistic model for t
he interactions between metal atoms in a system that is known to form metal
lic glasses; We find that although the CTRW model uses a pathological model
for the distribution of waiting times, the predictions of this theory are
much closer to the actual diffusion constants than those obtained via Zwanz
ig's model. We also find that there is a simple linear relationship between
the stretching parameter (beta) for Kohlrausch-Williams-Watts decay of the
cage correlation function and the dispersion parameter (gamma) that charac
terizes the "fractal" distribution of waiting times in the CTRW model.