Field theories and exact stochastic equations for interacting particle systems

TL;DR

This paper introduces a new field theory approach for analyzing the dynamics of interacting particle systems with reactions and diffusion, clarifying the role of stochastic equations and connecting to existing formalisms.

Contribution

It develops a general field theory from discrete stochastic processes, relating it to the Doi-Peliti formalism and large deviation techniques for non-equilibrium fluctuations.

Findings

Derived an exact stochastic equation for particle density fields.

Mapped the new field theory onto the Doi-Peliti formalism.

Clarified the nature of Langevin noise in reaction-diffusion systems.

Abstract

We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the 'imaginary' Langevin noise that appears in the context of reaction/diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of non-equilibrium systems in the hydrodynamic limit.