Fluctuation effects and multiscaling of the reaction-diffusion front for A+B to OE

We consider the properties of the diffusion-controlled reaction A+B to OE 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 mod x mod 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 mod x mod - 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 approximately B mod x mod - 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 mod x mod 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.