Effective Hardcore Exclusion Without Exclusion: Two-Species Pair Annihilation Revisited

Abstract: Reaction-diffusion systems with two species that mutually annihilate through $A+B\to\emptyset$ reactions display a slow decay of the total density $ρ$ which follows an anomalous power law in low dimensions. For hardcore particles in one dimension, this decay follows $ρ\sim t<sup>{-1/4}$ under symmetric diffusion and $ρ\sim t<sup>{-1/3}$ under asymmetric diffusion without relative bias between the two species. The $t<sup>{-1/3}$ behavior, in particular, has so far been observed exclusively in systems with hardcore exclusion. Here we construct a model of particles without hardcore exclusion that reproduces this same $t<sup>{-1/3}$ scaling. In our model, both species undergo asymmetric diffusion with a rate that depends nonlinearly on the local density, a form of transport that, in the absence of the other species, is superdiffusive and falls into the Kardar-Parisi-Zhang universality class. The scaling behavior of $t<sup>{-1/3}$ occurs when at least one of the two species undergoes asymmetric diffusion induced by microscopic processes involving pairs of particles, while asymmetric processes involving groups of three particles lead to $t<sup>{-1/4}$ scaling associated with symmetric diffusion. This demonstrates that the pair annihilation density decay exponent is not determined exclusively by the transport properties of the isolated particle species.