The A+B->0 annihilation reaction in a quenched random velocity field

Using field-theoretic renormalization group methods the long-time behaviour of the A + B -> O annihilation reaction with equal initial densities n(A)(0) = ng(0) = n(0) in a quenched random velocity field is studied. At every point (x, y) of a d-dimensional system the velocity is parallel or antiparallel to the x-axis and depends on the coordinates perpendicular to the flow. Assuming that upsilon(y) have zero mean and short-range correlations in the y-direction we show that the densities decay asymptotically as n(A,B)(t) similar or equal to An(0)(1/2)t(-(d+3)/8) for d < 3. The amplitude A is calculated at first order in epsilon = 3 - d.