DIFFUSION-LIMITED MANY-BODY REACTIONS IN ONE-DIMENSION AND THE METHOD OF INTERPARTICLE DISTRIBUTION-FUNCTIONS

The method of interparticle distribution functions (IPDF) has yielded several exact solutions of the kinetics of diffusion-limited reaction processes in one dimension. We generalize the IPDF method to the case where lattice sites may be occupied by more than one particle and apply it to the reaction processes nuA --> muA (nu > mu). We briefly review the case of nu = 2, for which the kinetics is anomalous, that is, does not agree with the predictions of classical rate equations. The case of nu = 3 is marginal. We compute the exact leading time behavior of the concentration decay, and the distribution of distances between nearest particles in the long time asymptotic limit. From the results of extensive numerical simulations, we observe the previously postulated logarithmic corrections to the concentration power-law decay. The case of nu > 3 is well described by classical rate equations. We show how this is expressed in the IPDF approach.