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 −eρ 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 ^κ|∂Λ|, where |∂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, ^κ(Γ) decreases to an asymptotic value ^κ(∞)∼^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^κ/ρ associated with charge fluctuations behaves very differently from that of the Debye length, ξ _D∼1/$\sqrt \Gamma$, which it approaches as Γ→0. The pair correlation function of the OCP is also studied.