Stretched exponential relaxation in a diffusive model for granular compaction

We studied the single dimer dynamics in a lattice diffusive model as a function of particle density in the high densification regime. The mean square displacement is found to be subdiffusive both in one and two dimen-sions. The spatial dependence of the self-part of the van Hove correlation function displays as a function of r a single peak and signals a dramatic slow down of the system for high density. The self-intermediate scattering function is fitted to the Kohlrausch-Williams-Watts law. The exponent b extracted from the fits is density independent while the relaxation time tfollows a scaling law with an exponent 2.5.