## Abstract

We analyze the limiting behavior of the densities ρ_{A}(t) and ρ_{B}(t), and the random spatial structure ξ(r) = (ξ_{A}(t)., ξ_{B}(t)), for the diffusion-controlled chemical reaction A+B→inert. For equal initial densities ρ_{B}(0) = ρ_{b}(0) there is a change in behavior from d≤ 4, where ρ_{A}(t) =ρ_{B}(t) ≈C/t^{d/4}, to d ≥ 4, where ρ_{A}(t) =ρ_{b}(t) ≈C/t as t → ∞; the term C depends on the initial densities and changes with d. There is a corresponding change in the spatial structure. In d < 4, the particle types separate with only one type present locally, and ξ, after suitable rescaling, tends to a random Gaussian process. In d >4, both particle types are, after large times, present locally in concentrations not depending on type or location. In d=4, both particle types are present locally, but with random concentrations, and the process tends to a limit.

Original language | English (US) |
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Pages (from-to) | 941-951 |

Number of pages | 11 |

Journal | Journal of Statistical Physics |

Volume | 65 |

Issue number | 5-6 |

DOIs | |

State | Published - Dec 1991 |

## Keywords

- Diffusion-limited reaction
- annihilating random walks
- asymptotic densities
- exact results
- spatial structure