Scaling Approach for the Kinetics of Recombination Processes

A scaling theory is developed to describe the time evolution of the irreversible diffusive recombination process A+B→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^-α for short times, crossing over to an exp(-At^α) decay for long times, with α=d/4 and α=(d+1)/4 for unbiased and biased diffusion, respectively.