Random walks on fractals and stretched exponential relaxation - art. no. 036131

Stretched exponential relaxation [exp-(t/tau)(betaK)] is observed in a larg e variety of systems but has not been explained so far. Studying random wal ks on percolation clusters in curved spaces whose dimensions range from 2 t o 7, we show that the relaxation is accurately a stretched exponential and is directly connected to the fractal nature of these clusters. Thus we find that in each dimension the decay exponent beta (K) is related to well-know n exponents of the percolation theory in the corresponding flat space. We s uggest that the stretched exponential behavior observed in many complex sys tems (polymers, colloids, glasses,...) is due to the fractal character of t heir configuration space.