Stochastic Field Theory for Transport Statistics in Diffusive Systems

TL;DR

This paper develops a universal field theory framework to analyze charge and current fluctuation statistics in diffusive systems, applicable across various physical scales and models.

Contribution

It introduces a saddle-point based field theory that simplifies the calculation of transport statistics using only local diffusion and noise parameters.

Findings

The theory provides a universal cumulant generating function for diffusive systems.

It applies to both mesoscopic and classical diffusive systems.

The approach simplifies the analysis of fluctuation statistics across different models.

Abstract

We present a field theory for the statistics of charge and current fluctuations in diffusive systems. The cumulant generating function is given by the saddle-point solution for the action of this field theory. The action depends on two parameters only: the local diffusion and noise coefficients, which naturally leads to the universality of the transport statistics for a wide class of multi-dimensional diffusive models. Our theory can be applied to semi-classical mesoscopic systems, as well as beyond mesoscopic physics.