Renormalization group approach to reaction-diffusion systems with input particles

We consider reaction-diffusion systems of a single species (A + A → φ) in the absence and the presence of a particle input. Applying renormalization group theory to a field theoretic description and matching theory to the renormalization group trajectory integrals of the systems, we find that for d < 2 in the absence of an input, the density decays as c(t) ∼ t^-ν with the dynamic exponent ν = d/2 and in the presence of input the density grows as c(I) ∼ I^μ with the static exponent μ = d/(d + 2), while for d > 2 the behaviors are mean-field like and for d = 2 there are logarithmic corrections to the mean-field results. The results for the absence of input are consistent with the previous results obtained using different methods. In addition, we propose a rigorous proof of Racz's conjecture about the relation between the static and the dynamic exponents, μ = ν/(1 + ν).