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Wilson renormalization of a reaction-diffusion process

F. van Wijland·K. Oerding·H. J. Hilhorst
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Abstract

Healthy and sick individuals (A and B particles) diffuse independently with diffusion constants D_A and D_B. Sick individuals upon encounter infect healthy ones (at rate k), but may also spontaneously recover (at rate 1/τ). The propagation of the epidemic therefore couples to the fluctuations in the total population density. Global extinction occurs below a critical value ρ_{c} of the spatially averaged total density. The epidemic evolves as the diffusion--reaction--decay process A + B --> 2B, B --> A , for which we write down the field theory. The stationary state properties of this theory when D_A=D_B were obtained by Kree et al. The critical behavior for D_A D_B remains unsolved.

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F. van Wijland, K. Oerding, H. J. Hilhorst. 1997-06-19. Wilson renormalization of a reaction-diffusion process. https://doi.org/10.1016/s0378-4371(97)00603-1

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