Dynamics of interacting particle systems: stochastic process and field theory

TL;DR

This paper introduces a stochastic process and field theory approach to analyze interacting particle systems, clarifying their duality, the Cole-Hopf map, and imaginary noises, with applications to zero range processes and large deviations.

Contribution

It develops a new field theory framework based on stochastic considerations that directly focuses on density fields, providing insights into duality and noise phenomena in particle systems.

Findings

Derived path integral formulas from stochastic considerations.

Clarified the duality between the new field theory and the Doi-Peliti approach.

Applied the framework to zero range processes and large deviation analysis.

Abstract

We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of Doi and Peliti. This clarify both the origin of the Cole-Hopf map between the two approaches and the occurence of imaginary noises in effective Langevin equations for reaction-diffusion systems. The advantage of our approach is that it focuses directly on the density field. We show some applications, in particular on the Zero Range Process, hydrodynamic limits and large deviation functional.