Effective Hardcore Exclusion Without Exclusion: Two-Species Pair Annihilation Revisited
Abstract
Reaction-diffusion systems with two species that mutually annihilate through A+B→∅ 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∼ t−1/4 under symmetric diffusion and ρ∼ t−1/3 under asymmetric diffusion without relative bias between the two species. The t−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−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−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−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.
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BibTeX
@misc{park2026effective,
title = {{Effective Hardcore Exclusion Without Exclusion: Two-Species Pair Annihilation Revisited}},
author = {Su-Chan Park and Foster Thompson},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30630},
eprint = {2608.30630},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30630},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Effective Hardcore Exclusion Without Exclusion: Two-Species Pair Annihilation Revisited
AU - Su-Chan Park
AU - Foster Thompson
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30630
UR - https://arxiv.org/abs/2608.30630
AB - Reaction-diffusion systems with two species that mutually annihilate through A+B→∅ 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∼ t^−1/4 under symmetric diffusion and ρ∼ t^−1/3 under asymmetric diffusion without relative bias between the two species. The t^−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^−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^−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^−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.
ER -