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

Abstract

We analyze the annihilation of equally-charged particles based on the Brownian motion model built by F. 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 $\beta =q^2/(k_{B}T)$. We derive an analytical approach in order to describe the large-$t$ asymptotic behaviour for the number density decay, which can be described as a power law, i.e., $n\sim t^{-\nu }$. 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.

arXiv comment10 pages, 6 figures

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• Annihilation of Charged Particles
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Cited by in corpus (1)

• Dynamical fluctuations in the Riesz gas