Front propagation in an A→2A, A→3A process in one dimension: velocity, diffusion, and velocity correlations

We study front propagation in the reaction-diffusion process {A→[over ε]2A,A→[over ε(t)]3A} on a one-dimensional lattice with hard-core interactions between the particles. Using the leading particle picture, the velocity of the front is computed using different approximate methods that yield results in good agreement with simulation results. We observe that the front dynamics exhibits temporal velocity correlations that must be accounted for to obtain accurate estimates of the front diffusion coefficient. Interestingly, these temporal correlations change sign depending upon the sign of ε(t)-D, where D is the bare diffusion coefficient of A particles. For ε(t)=D, we find analytically as well as numerically that the leading particle and thus the front move as an uncorrelated random walker.