The reaction process A+A -> O in Sinai disorder

The single-species reaction-diffusion process A+A --> O is examined in the presence of an uncorrelated, quenched random velocity field. Utilizing a fi eld-theoretic approach, we find that in two dimensions and below the densit y decay is altered from the case of purely diffusing reactants. In two dime nsions the density amplitude is reduced in the presence of weak disorder, y ielding the interesting result that Sinai disorder can cause reactions to o ccur at an increased rate. This is in contrast to the case of long-range co rrelated disorder, where it was shown that the reaction becomes sub-diffusi on limited. However, when written in terms of the microscopic diffusion con stant it is seen that increasing the disorder has the effect of reducing th e rate of the reaction. Below two dimensions, the effect of Sinai disorder is much more severe and the reaction is shown to become sub-diffusion limit ed. Although there is no universal amplitude for the time-dependence of the density, it is universal when expressed in terms of the disorder-averaged diffusion length. The appropriate amplitude is calculated to one-loop order .