REPLICA-SCALING ANALYSIS OF DIFFUSION IN QUENCHED CORRELATED RANDOM-MEDIA

We propose a unifying picture of d-dimensional diffusion in randomly correlated media Z(x,t) = D-DELTA-Z + V(x)Z using the replica-scaling method of Zhang [Phys. Rev. B 42, 4897 (1990)]. Here V(x) denotes a frozen random potential of strength-lambda and correlation length a and arbitrary variance [V(x)V(0)] = lambda-2R(a)(x). We are interested in the temporal dependence of [Z(n)] and the diffusion law. It is demonstrated, in particular, that for the special case of uncorrelated disorder the asymptotic behavior is given by ln[Z(n)] congruent-to lambda-2a(-d)n2t2, recovering the earlier result of Zeldovich et al [Sov. Phys. JETP 62, 1188 (1985)], whereas at intermediate times nt less-than-or-equal-to Da(d-2)/lambda-2 the situation is dimension dependent: we obtain ln[Z(n)] congruent-to (lambda-4/D(d))1/(2-d)(nt)(4-d)/(2-d) for d < 2 and ln[Z(n)] congruent-to - n for d > 4. For 2 < d < 4 we conclude that ln[Z(n)] congruent-to lambda-2D(-d/2)n2t2-(d/2) if t < a2/D. The relation between the temporal dependence of [Z(n)] and the diffusion law is also established. These results are expected to be as accurate as other Flory-like theories.