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

A. Alastuey, V. Ballenegger, and D. Wendland
Phys. Rev. E 102, 023203 – Published 10 August 2020

Abstract

We consider a quantum multicomponent 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 nonperturbative 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 because of a Debye-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 (S1) 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.

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  • Received 26 May 2020
  • Accepted 9 July 2020

DOI:https://doi.org/10.1103/PhysRevE.102.023203

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Plasma Physics

Authors & Affiliations

A. Alastuey1, V. Ballenegger2, and D. Wendland1,2

  • 1Laboratoire de Physique, ENS Lyon, UMR CNRS 5672 46 allée d'Italie, 69364 Lyon Cedex 07, France
  • 2Institut UTINAM, Univ. Bourgogne-Franche-Comté, UMR CNRS 6213 16, route de Gray, 25030 Besançon Cedex, France

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Vol. 102, Iss. 2 — August 2020

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