RENORMALIZATION-GROUP ANALYSIS OF SUPERDIFFUSION IN RANDOM VELOCITY-FIELDS

Field-theoretic renormalization group theory is applied to the analysis of the asymptotic behaviour of diffusion in random velocity fields, each non-vanishing component of which is independent of the coordinate along the direction of that component. Below the critical dimension d(c) = 3, the corresponding field theory is shown to have a non-trivial infrared stable fixed point of the renormalization group, which controls the long-time, large-distance behaviour of the model. The anomalous dimension-nu has been found exactly in the epsilon = 3 - d expansion, and the leading logarithmic corrections to the normal diffusion at d = 3 have been determined for all d': 1 less-than-or-equal-to d' less-than-or-equal-to d, where d' is the number of components of the drift field.