Fluctuation kinetics in a multispecies reaction-diffusion system

We study fluctuation effects in a two-species reaction-diffusion system, with three competing reactions A + A -> 0, B + B --> 0 and A + B --> 0. Asymptotic density decay rates are calculated for d less than or equal to 2 using two separate methods-the Smoluchowski approximation and also field-theoretic-renormalization group (RG) techniques. Both approaches predict power-law decays, with exponents which depend asymptotically only on the ratio of diffusion constants, and not on the reaction rates. Furthermore, we find that, for d < 2, the Smoluchowski approximation and the RG improved tree level give identical exponents. However, whereas the Smoluchowski approach cannot easily be improved, we show that the RG provides a systematic method for incorporating additional fluctuation effects. We demonstrate this advantage by evaluating one-loop corrections for the exponents in d < 2 and find good agreement with simulations and exact results.