Fluctuations and the role of collision duration in reaction-diffusion systems

Abstract

In a reaction-diffusion system, fluctuations in both diffusion and reaction events have important effects on the steady-state statistics of the system. Here, we argue through extensive lattice simulations, mean-field–type arguments, and the Doi-Peliti formalism that the collision duration statistics —i.e., the time two particles stay together in a lattice site—plays a leading role in determining the steady state of the system. We obtain approximate expressions for the average densities of the chemical species and for the critical diffusion coefficient required to sustain the reaction.