Fluctuation kinetics in a multispecies reaction - diffusion system

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Abstract
We study fluctuation effects in a two-species reaction - diffusion system, with three competing reactions , and . Asymptotic density decay rates are calculated for 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.
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