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 $\beta$, defined as $\beta =q^2/\left(k_{B}T\right)$. 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, $n\sim t^{-\nu }$. For a sufficiently large $\beta$, the power-law exponent $\nu$ behaves as ${(\beta +1)}^{-1}$, which was corroborated through several computational simulations. For small $\beta$, in the diffusive regime, we recover the exponent of 1/2 as predicted by single-species uncharged annihilation.

• Received 21 September 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012112