Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes

TL;DR

This paper extends quantum stochastic processes to model reaction diffusion systems, providing new analytical tools for spatial birth-death processes that complement traditional master equations and path integral methods.

Contribution

It introduces an extension of quantum stochastic noises to reaction diffusion systems, offering an alternative analytical framework for spatial birth-death processes.

Findings

Extended quantum noises model reaction diffusion systems

Provides efficient analysis methods for spatial birth-death processes

Offers an alternative to master equations and path integrals

Abstract

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is shown that the three standard noises of quantum stochastic processes can be extended to model reaction diffusion systems, the methods being exemplified with spatial birth-death processes. The usual approach for these systems are master equations, or Doi-Peliti path integration techniques. The machinery described here provide efficient analyses for many systems of interest, and offer an alternative set of tools to investigate such problems.