The charge fluctuations in classical Coulomb systems

Abstract

We study the asymptotic behavior of the charge fluctuations 〈(Q Λ − 〈(Q Λ〉)2〉 in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge fluctuations are not extensive, then they are necessarily of the order of the surface ¦∂λ¦. Moreover, when the canonical sum rules that are typical for equilibrium states of particles interacting with long-range forces hold true, we prove a central limit theorem for the normalized charge variable ¦∂λ¦−1/2(〈(Q Λ − 〈(Q Λ〉)) in two and three dimensions. In one dimension, the probability distribution of the charge itself converges. The latter case is illustrated by the example of the one-dimensional Coulomb gas.