Biased Diffusion with Correlated Noise

TL;DR

This paper investigates how long-range correlated noise influences the large-scale behavior of biased diffusion of particles, revealing complex stability exchanges and crossover phenomena in different dimensions.

Contribution

It introduces a renormalization group analysis of biased diffusion with correlated noise, highlighting the relevance of long-range correlations and the resulting universality class transitions.

Findings

Long-range noise is relevant above a critical dimension.

Multiple stability exchanges between fixed points occur as noise correlation range varies.

Crossover phenomena between universality classes are observed.

Abstract

The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension $d_{LR}$, the long-ranged noise is always relevant. In contrast, for $d<d_{LR}$, we find a ``weak noise'' regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems.