62 v 2 2 6 A ug 1 99 6 The A + B → ∅ annihilation reaction in a quenched random velocity field

Using field-theoretic renormalization group methods the long-time behaviour of the A + B → ∅ annihilation reaction with equal initial densities n A (0) = n B (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 v(y) have zero mean and short-range correlations in the y-direction we show that the densities decay asymptotically as n A,B (t) ≃ An 1/2 0 t −(d+3)/8 for d < 3. The amplitude A is calculated at first order in ǫ = 3 − d.