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

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 renormalization-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\(-mu), where mu = 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 similar to B\x\(-mu-2). For d > 2, we find similar power laws with mu = 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 integral \x\(q)R(x,t) dx fail to satisfy simple scaling for q > mu + 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.