Doi-Peliti Path Integral Methods for Stochastic Systems with Partial Exclusion

TL;DR

This paper develops Doi-Peliti path integral methods for stochastic systems with limited site occupation, introducing a generalized framework and demonstrating perturbative and exact summation techniques for specific models.

Contribution

It extends Doi-Peliti methods to systems with partial exclusion, providing a unified framework and novel path integral formulations using paragrassmannian techniques.

Findings

Magnus expansion is often needed for constructing actions.

Perturbative techniques are effective for many models.

Some models allow exact summation of expansions.

Abstract

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.