ON THE SCALE-INVARIANT DISTRIBUTION OF THE DIFFUSION-COEFFICIENT FOR CLASSICAL PARTICLES DIFFUSING IN DISORDERED MEDIA

The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d = 0 is applied to the distribution P(D) using the n-replica approach. In the annealed approximation (n = 1), the inverse Gaussian distribution is found to be the stable one under rescaling. This identification is based on symmetry arguments and subtle relations between this model and that of fluctuating interfaces studied by Wallace and Zia. The renormalization-group flow for the ratios between subsequent cumulants shows a regime of pure diffusion for small disorder, where P(D) --> delta(D - D), and a regime of strong disorder in which the cumulants grow infinitely large and the diffusion process is ill defined. The boundary between these two regimes is associated with an unstable fixed-point and subdiffusive behaviour [x2] approximately t1-d/2. For the quenched (n --> 0) case we find that unphysical operators are generated raising doubts on the renormalizability of this model. Implications for other random systems near their lower critical dimension are discussed.