Scaling Approach for the Kinetics of Recombination Processes

Abstract

A scaling theory is developed to describe the time evolution of the irreversible diffusive recombination process $A+B\to \mathrm{inert}$. Fluctuations are shown to alter radically the decay laws predicted from the rate-equation approach. For unequal initial densities, the minority species is predicted to decay as $t^{-\alpha }$ for short times, crossing over to an $\exp (-A{t}^{\alpha })$ decay for long times, with $\alpha =\frac{d}{4}$ and $\alpha =\frac{\mathrm{}(d+1\mathrm{})\mathrm{}}{4}$ for unbiased and biased diffusion, respectively.