Classical Coulomb Systems:Screening and Correlations Revisited

TL;DR

This paper revisits classical Coulomb systems, emphasizing the universal nature of screening and long-range correlations, and derives explicit results for surface charge fluctuations using electrostatic principles.

Contribution

It provides a unified derivation of universal properties of Coulomb systems based on electrostatics, with explicit results for simple geometries and Gaussian fluctuation assumptions.

Findings

Universal long-range correlations in potentials and fields

Explicit surface charge fluctuation results for simple geometries

Gaussian fluctuation behavior with short-distance cutoff

Abstract

From the laws of macroscopic electrostatics of conductors (in particular the existence of screening) taken for granted, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The universality is especially apparent in the long-range correlations of the electrical potentials and fields. The charge fluctuations are derived from the field fluctuations. This is a convenient way for studying the surface charge fluctuations on a conductor with boundaries. Explicit results are given for simple geometries. The potentials and the fields have Gaussian fluctuations, except for a short-distance cutoff.