Crossover from rate-equation to diffusion-controlled kinetics in two-particle coagulation

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Abstract
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A→A with partial reaction probabilities on particle encounters which are otherwise hard core. The present approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximation becomes quantitatively accurate when the system is initially close to the continuum behavior, i.e., for small initial density and fast reactions. For large initial density and slow reactions, lattice effects are non-negligible for an extended initial time interval. In such cases, our approximation provides a correct description of the initial mean field as well as the asymptotic large-time, fluctuation-dominated behavior. However, the intermediate-time crossover between the two regimes is described only semiquantitatively.
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