Diffusion-limited reaction under quenched disorder

We have studied diffusion-limited reaction on a one-dimensional lattice under the quenched disorder using Monte Carlo simulations. The hopping probabilities at a site is distributed by the power law p(y) = vy(v-1) with 0 < v <less than or equal to> 1 and 0 < y <less than or equal to> 1. The density of the reactants decays according to a power law, C(t)similar to t(-alpha (v)) for A +A --> 0 and A + B --> 0 annihilation reaction. The exponent alpha (v) depends on the disorder exponent v. For A +A --> 0, we have found alpha (v)= v/(1 + v). For A + B --> 0, we have observed alpha = 0.25 at v > 0.4 and alpha decreases monotonically for alpha < 0.4. (C) 2001 Elsevier Science B.V. All rights reserved.