Langevin dynamics of A+A reactions in one dimension

Abstract

We propose a set of Langevin equations of motion together with a reaction rule for the study of binary reactions. Our scheme is designed to address this problem for arbitrary friction ° and temperature T. It easily accommodates the inclusion of a substrate potential, and it lends itself to straightforward numerical integration. We test this approach on di®usion-limited (° ! 1) as well as ballistic (° = 0) A+A ! P reactions for which there are extensive exact and approximate theoretical results as well as extensive Monte Carlo results. We reproduce the known results using our integration scheme, and also present new results for the ballistic reactions.