Anomalous Dimension in a Two-Species Reaction-Diffusion Model

We consider particles ($A$) diffusing in the presence of traps ($B$), which themselves are diffusing and reacting, i.e. the two-species reaction diffusion model $A+B\to B$ and $B+B\to(0,B)$. We introduce a simulation technique that provides the full probability distribution of particles for a given realization of the trap dynamics. Previous renormalization group analysis predicted that the density of $A$ particles decays as $a~t^{-\theta}$ where $\theta$ is a nontrivial, universal exponent for $d<2$. We compare our results with these predictions, and also demonstrate the scaling of the correlation functions. We discover an anomalous dimension in the particle-particle correlation function, described by $G_{AA}(0)\sim t^\phi$, and we report our measurements for this new exponent.