Reaction diffusion systems and extensions of quantum stochastic processes

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued Ito 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.

Automated summary

Reaction diffusion systems can be modeled using the machinery of quantum stochastic processes, which generalize Brownian motion and Poisson processes. This approach provides efficient analyses and alternative tools for investigating these systems, exemplified with spatial birth-death processes. The usual methods for such systems are master equations or Doi-Peliti path integration techniques.