Langevin equations for reaction-diffusion processes

TL;DR

This paper derives exact Langevin equations for reaction-diffusion processes with bimolecular reactants, enabling better numerical and theoretical analysis while clarifying conceptual issues in field theory.

Contribution

It introduces well-behaved Langevin equations for reaction-diffusion systems, facilitating systematic analysis and resolving longstanding conceptual challenges.

Findings

Derived exact Langevin equations for bimolecular reaction-diffusion processes

Showed how to compute particle numbers using duality relations

Clarified conceptual issues in field-theoretical approaches

Abstract

For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.