FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0

Abstract

We consider the properties of the diffusion controlled reaction A+B->0 in the steady state, where fixed currents of A and B particles are maintained at opposite edges of the system. Using renormalisation group methods, we explicitly calculate the asymptotic forms of the reaction front and particle densities as expansions in (JD^{-1}|x|^{d+1})^{-1}, where J are the (equal) applied currents, and D the (equal) diffusion constants. For the asymptotic densities of the minority species, we find, in addition to the expected exponential decay, fluctuation induced power law tails, which, for d<2, have a universal form A|x|^{-omega}, where omega=5+O(epsilon), and epsilon=2-d. A related expansion is derived for the reaction rate profile R, where we find the asymptotic power law R \sim B|x|^{-omega -2}. For d>2, we find similar power laws with omega=d+3, but with non-universal coefficients. Logarithmic corrections occur in d=2. These results imply that, in the time dependent case, with segregated initial conditions, the moments \int |x|^{q}R(x,t)dx fail to satisfy simple scaling for q>omega+1. Finally, it is shown that the fluctuation induced wandering of the position of the reaction front centre may be neglected for large enough systems.