Screened activity expansion for the grand-potential of a quantum plasma and how to derive approximate equations of state compatible with electroneutrality

TL;DR

This paper develops a non-perturbative screened activity series for quantum plasmas' pressure, enabling the derivation of approximate, electroneutral equations of state that incorporate complex particle interactions and recombination effects.

Contribution

It introduces a new neutralization scheme for equations of state in quantum plasmas, ensuring electroneutrality automatically within a screened activity series framework.

Findings

Series is non-perturbative and involves few diagrams at each order.

Particle densities satisfy local charge neutrality via Debye screening.

Method can incorporate recombined entities with three or more particles.

Abstract

We consider a quantum multi-component plasma made with S species of point charged particles interacting via the Coulomb potential. We derive the screened activity series for the pressure in the grand-canonical ensemble within the Feynman-Kac path integral representation of the system in terms of a classical gas of loops. This series is useful for computing equations of state for it is non-perturbative with respect to the strength of the interaction and it involves relatively few diagrams at a given order. The known screened activity series for the particle densities can be recovered by differentiation. The particle densities satisfy local charge neutrality thanks to a Debye-screening dressing mechanism of the diagrams in these series. We introduce a new general neutralization prescription, based on this mechanism, for deriving approximate equations of state where consistency with electroneutrality is automatically ensured. This prescription is compared to other ones, including a neutralization scheme inspired by the Lieb-Lebowitz theorem and based on the introduction of (S -- 1) suitable independent combinations of the activities. Eventually, we briefly argue how the activity series for the pressure, combined with the Debye-dressing prescription, can be used for deriving approximate equations of state at moderate densities, which include the contributions of recombined entities made with three or more particles.