Imaginary noise and parity conservation in the reaction A+A <--> 0

TL;DR

This paper explores the complex stochastic dynamics of a reversible reaction using Poisson representation and Langevin equations with imaginary noise, revealing unique probability flow features in reaction-diffusion systems.

Contribution

It introduces an analysis of imaginary noise Langevin equations in reaction-diffusion models, highlighting novel probability flow behaviors in the complex plane.

Findings

Complex probability flow exhibits curious features.

Imaginary noise Langevin equations are relevant in reaction-diffusion field theories.

Analytical and simulation results confirm the unique flow patterns.

Abstract

The master equation for the reversible reaction A+A <--> 0 is considered in Poisson representation, where it is equivalent to a Langevin equation with imaginary noise for a complex stochastic variable \phi. Such Langevin equations appear quite generally in field-theoretic treatments of reaction-diffusion problems. For this example we study the probability flow in the complex \phi plane both analytically and by simulation. We show that this flow has various curious features that must be expected to occur similarly in other Langevin equations associated with reaction-diffusion problems.