Reaction-diffusion front forA+B→∅in one dimension

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\to \varnothing$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal diffusion constants $D$, we find that when $\lambda J^{-\frac{1}{2}}{D}^{-\frac{1}{2}}\ll 1$ the reaction front is well described by mean-field theory. However, for $\lambda J^{-\frac{1}{2}}{D}^{-\frac{1}{2}}\gg 1$, the front acquires a Gaussian profile—a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (nonwandering) front width and find results consistent with scaling and field theoretic predictions.