Biased diffusion in percolation systems: Indication of multifractal behaviour

The authors study diffusion in percolation systems at criticality in the presence of a constant bias field E. Using the exact enumeration method they show that the mean displacement of a random walker varies as (r(t)) approximately log t/A(E) where A/(E)=In((1+E)/(1-E)) for small E. More generally, diffusion on a given configuration is characterised by the probability P(r,t) that the random walker is on site r at time t. They find that the corresponding configurational average shows simple scaling behaviour and is described by a single exponent. In contrast their numerical results indicate that the averaged moments (P^q(t))= Sigma _rP ^q(r,t)) are described by an infinite hierarchy of exponents. For zero bias field, however, all moments are determined by a single gap exponent.