Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

TL;DR

This paper generalizes the Stillinger-Lovett sum rule for a guest charge in a 2D Coulomb system, deriving moments of the screening cloud and potential, with explicit results in special cases.

Contribution

It provides a simplified derivation of the second moment sum rule and extends the analysis to the zeroth moment in two-component plasmas using the BGY hierarchy.

Findings

Generalized sum rule for the second moment of the screening cloud

Explicit expressions for moments of the electric potential

Relations between potential moments and excess chemical potential

Abstract

A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases.