Reaction diffusion systems and extensions of quantum stochastic processes

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

Original languageEnglish
Article number235002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number23
Early online date18 May 2023
Publication statusPublished - 6 Jun 2023


  • Doi-Peliti
  • birth-death process
  • path integration
  • quantum stochastic process
  • reaction-diffusion

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