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arXiv · 2212.10864

Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes

Chris D Greenman
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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.

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Chris D Greenman. 2022-12-21. Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes. https://doi.org/10.1088/1751-8121/acd288

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