Fourth moment sum rule for the charge correlations of a two-component classical plasma

TL;DR

This paper derives a sum rule for the fourth moment of charge correlations in a two-component ionic fluid using density functional theory and linear response, linking it to thermodynamic properties and confirming the Stillinger-Lovett condition.

Contribution

It introduces a new thermodynamic expression for the fourth moment sum rule of charge correlations in ionic fluids, extending understanding of conducting phases.

Findings

Derived a sum rule for the fourth moment of charge correlations.

Connected the sum rule to thermodynamic quantities like compressibility.

Confirmed the Stillinger-Lovett condition and its applicability near critical points.

Abstract

We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.