Charge Fluctuations in the Two-Dimensional One-Component Plasma

Abstract

We study, via computer simulations, the fluctuations in the net electric charge, in a two dimensional one component plasma (OCP) with uniform background charge density $-e ρ$, in a region $Λ$ inside a much larger overall neutral system. Setting $e=1$ this is the same as the fluctuations in $N_Λ$, the number of mobile particles of charge $e$. As expected the distribution of $ N_Λ$ has, for large $Λ$, a Gaussian form with a variance which grows only as $\hat κ|\partial Λ|$, where $|\partial Λ|$ is the length of the perimeter of $Λ$. The properties of this system depend only on the coupling parameter $Γ= kT$ which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter $Γ$ increases, $\hat κ(Γ)$ decreases to an asymptotic value $\hat κ(\infty) \sim \hat κ(2)/2$ which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large $Γ$, the characteristic length $ξ_L = 2\hat κ/ρ$ associated with charge fluctuations behaves very differently from that of the Debye length, $ξ_D \sim 1/\sqrt Γ$, which it approaches as $Γ\to 0$. The pair correlation function of the OCP is also studied.