Diffusion-limitedA+B→0 reaction: Correlated initial condition

We find a time dependence different from that reported previously in the literature for the species concentration in the A+B→0 diffusion-limited reaction for dimensions d<2 when the A-B pairs are initially correlated. Whereas an uncorrelated initial distribution leads to the well-known decay law ρ∼${\mathit{t}}^{\mathrm{-}\mathit{d}/4\mathrm{}}$ for d<4 and ρ∼${\mathit{t}}^{\mathrm{-}1}$ for d≥4, a correlated initial distribution leads to the decay law ρ∼${\mathit{t}}^{\mathrm{-}(\mathit{d}+2)/4\mathrm{}}$ for d<2 and ρ∼${\mathit{t}}^{\mathrm{-}1}$ for d≥2. The decay is therefore more rapid in the correlated case and the critical dimension for ‘‘anomalous’’ behavior shifts from 4 to 2.