A renormalization group study of a class of reaction-diffusion model, with particles input

Details A renormalization group study of a class of reaction-diffusion model, with particles input A renormalization group study of a class of reaction-diffusion model, with particles input

1996-09-10

arxiv.org/abs/cond-mat/9609088v1

J. Phys. A: Math. Gen. 30, 1101 (1997)

Physics

Condensed Matter

Ten pages, using Latex and IOP macro. Two latex figures. Submitted to Journal of Physics A. Also available at http://mykonos

Scientific paper

10.1088/0305-4470/30/4/013

We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate $J$. For dimension $d\leq 2$, the dynamics strongly depends on the fluctuations while, for $d >2$, the behaviour is mean-field like. The models are mapped onto a field theory which properties are studied in a renormalization group approach. Simple relations are found between the time-dependent correlation functions of the different models of the class. For the pure coagulation-diffusion model the time-dependent density is found to be of the form $c(t,J,D) = (J/D)^{1/\delta}{\cal F}[(J/D)^{\Delta} Dt]$, where $D$ is the diffusion constant. The critical exponent $\delta$ and $\Delta$ are computed to all orders in $\epsilon=2-d$, where $d$ is the dimension of the system, while the scaling function $\cal F$ is computed to second order in $\epsilon$. For the one-dimensional case an exact analytical solution is provided which predictions are compared with the results of the renormalization group approach for $\epsilon=1$.

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