Numerical Measurement of the Anomalous Dimension in a Two-Species Reaction-Diffusion Model

We consider a two-species reaction-diffusion model that consists of the trapping reaction A+B→A with traps that either annihilate A+A→0 or coalesce A+A→A. Both species undergo diffusion with distinct diffusion constants D_A and D_B. We introduce a simulation technique that provides the full probability distribution of B particles for a given realization of the trap dynamics, greatly improving statistical accuracy. We measure in one dimension the B particle density decay exponent and the recently predicted anomalous dimension φ that appears in the asymptotic B particle correlation function C_BB(r,t) ∼ t^φ f(r/t^1/2). These exponents are predicted via renormalization group calculations to be universal for dimensions d≤2, depending only on the diffusion constant ratio and the trap reaction type. We compare our measured values to the renormalization group predictions, and to various exact solutions based on 3-walker and 4-walker problems.