A RENORMALIZATION-GROUP STUDY OF A CLASS OF REACTION-DIFFUSION MODELS, WITH PARTICLES INPUT

We study a class of reaction-diffusion models extrapolating continuous ly between the pure coagulation-diffusion case (A + A --> A) and the p ure annihilation-diffusion one (A + A --> O) with particles input (O - -> A) at a rate J. For dimension d less than or equal to 2, the dynami cs strongly depends on the fluctuations while, for d > 2, the behaviou r is mean-field like. The models are mapped onto a field theory whose properties are studied in a renormalization group approach. Simple rel ations are found between the time-dependent correlation functions of t he different models of the class. For the pure coagulation-diffusion m odel the time-dependent density is found to be of the form c(t, J, D) = (J/D)F-l/delta[(J/D)(Delta)Dt], where D is the diffusion constant. T he critical exponent delta and Delta are computed to all orders in eps ilon = 2 - d, where d is the dimension of the system, while the scalin g function F is computed to second order in epsilon. For the one-dimen sional case an exact analytical solution is provided whose predictions are compared with the results of the renormalization group approach f or epsilon = 1.