Mixing in reaction dynamics under enhanced diffusion conditions

We first review the Levy-flight approach for the description of enhanced diffusion and then study the effects of mixing on the transient A + B --> 0 reaction at stoichiometric conditions in d = 1-3 dimensions under enhanced diffusion conditions; The particles are assumed to follow Levy walks, characterized by an index , which result in enhanced diffusion for 1 < gamma < 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction-diffusion equations and computer simulations of this multi-particle problem. We concentrate on the segregation phenomenon and demonstrate that, depending on gamma, segregation may disappear in d = 3 dimensions under enhanced diffusion conditions. Hence, Levy walks lead to an efficient mixing of reacting particles.