Extinction and survival in two-species annihilation

Annihilation of single-species charged particles based on Dyson gas dynamics

We analyze the annihilation of equally charged particles based on the Brownian motion model built by Dyson for N particles with charge q interacting via the log-Coulomb potential on the unitary circle at a reduced inverse temperature β, defined as β=q^{2}/(k_{B}T). We derive an analytical approach to describe the large-t asymptotic behavior for the number density decay, which can be described as a power law, n∼t^{-ν}. For a sufficiently large β, the power-law exponent ν behaves as (β+1)^{-1}, which was corroborated through several computational simulations. For small β, in the diffusive regime, we recover the exponent of 1/2 as predicted by single-species uncharged annihilation.