Random walk in random environment with constrained long-range correlated drift forces

Abstract

A renormalisation group analysis of diffusion in random medium with long-range correlations is presented. Random drift with independent divergence-free and curl-free parts is shown to lead to non-universal anomalous diffusive behaviour, the character of which depends on the relative strength of the components of the drift. In the case of divergence-free drift, superdiffusive long-time behaviour is shown to take place, the anomalous dimension of which is determined exactly by the fixed point equation of the renormalisation group.