Annihilation of Charged Particles

TL;DR

This paper investigates the irreversible annihilation kinetics of charged particles with long-range interactions, revealing different decay behaviors depending on the interaction exponent and system dimensionality.

Contribution

It provides a detailed analysis of how the decay of particle density varies with the interaction exponent in one-dimensional systems, including logarithmic corrections.

Findings

Density decays as $t^{-1/(2+\lambda)}$ for $\lambda>1$

Density decays as $t^{-1/(1+2\lambda)}$ for $1/2<\lambda<1$

Asymptotic behavior depends on system size for $\lambda \\leq 1/2$

Abstract

The kinetics of irreversible annihilation of charged particles performing overdamped motion induced by long-range interaction force, $F(r)\sim r^{-\lambda}$, is investigated. The system exhibits rich kinetic behaviors depending on the force exponent $\lambda$. In one dimension we find that the densities decay as $t^{-1/(2+\lambda)}$ and $t^{-1/(1+2\lambda)}$ when $\lambda>1$ and $1/2<\lambda<1$, respectively, with logarithmic correction at $\lambda=1$. For $\lambda \leq 1/2$, the asymptotic behavior is shown to be dependent on system size.