Diffusion-limited reaction in the presence of random fields and transition rates

Abstract

The diffusion-limited reaction was studied on a one-dimensional lattice in the presence of random fields and transition rates using Monte Carlo simulations. In the case of transition rates the hopping probabilities at a site are distributed according to the power law p(y)=νyν−1 with 0<ν⩽1 and 0<y⩽1. The density of the reactants decays according to a power-law, C(t)∼t−α(ν) for A+A→0 and A+B→0 annihilation reactions. The exponent α(ν) depends on the disorder exponent ν. For A+A→0, we found α(ν)=ν/(1+ν). For A+B→0, we observed α=0.25 at ν>0.4 and α decreases monotonically for ν<0.4. In the case of the random fields the density decays according to C(t)∼[b(E)/log(t)]2 regardless of the strength of the random fields E for A+A→0 and A+A→A reactions, where b(E)∼log[(1+E)/(1−E)]. The diffusion-limited coagulation A+A→A belongs to the same universality class as the A+A→0 reaction under the random fields. For A+B→0 annihilations we observe that the density decays according to C(t)∼b(E)/log(t) in the presence of the random fields.