Annihilation of Charged Particles

Abstract

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