Current distribution in systems with anomalous diffusion: renormalisation group approach

TL;DR

This paper uses renormalisation group methods to analyze the large deviation function of particle current in systems with anomalous diffusion, revealing universal scaling laws governed by known exponents.

Contribution

It introduces a systematic RG approach to determine power laws in current large deviation functions for various anomalous diffusion systems.

Findings

Large deviation functions follow universal scaling laws.

Anomalous dimensions of noise correlators govern the behavior.

Method applies to diverse non-equilibrium systems.

Abstract

We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study include mutually repelling particles with a drift, a driven lattice gas displaying a continuous nonequilibrium phase transition, and particles diffusing in a anisotropic random advective field. It is exemplified how renormalisation group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We show that the latter are governed by known universal scaling exponents, specifically, the anomalous dimension of the noise correlators.