Two Langevin equations in the Doi-Peliti formalism

TL;DR

This paper introduces a novel system-size expansion within the Doi-Peliti formalism, revealing a connection between two Langevin equations related to stochastic chemical kinetics and density fluctuations.

Contribution

It presents a new decomposition of unity via Cole-Hopf transformation, linking different Langevin equations in the Doi-Peliti framework.

Findings

Clarifies the relationship between Langevin equations for density fluctuations and path-integral expressions

Applies the method to a simple reaction scheme to demonstrate its effectiveness

Provides insights into stochastic chemical kinetics modeling

Abstract

A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \rightleftarrows X+X$ is investigated as an illustrative example.