Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes

Abstract

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.

29 pages

References in corpus (8)

• Dynamic first-order phase transition in kinetically constrained models of glasses
• Quantum stochastic processes and quantum non-Markovian phenomena
• Stochastic population dynamics in spatially extended predator-prey systems
• A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations
• A kinetic theory for age-structured stochastic birth-death processes
• Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigration
• Doi-Peliti Path Integral Methods for Stochastic Systems with Partial Exclusion
• Duality relations between spatial birth-death processes and diffusions in Hilbert space