An introduction to quantum plasmas

TL;DR

This paper introduces quantum plasmas, comparing shielding effects in different regimes, and derives models like the Wigner-Poisson system and quantum hydrodynamics, discussing their advantages and limitations.

Contribution

It provides a detailed derivation of quantum plasma models from fundamental principles, clarifying their applicability and limitations.

Findings

Derivation of the Wigner-Poisson system for quantum plasmas

Development of a quantum hydrodynamic model from the Wigner-Poisson system

Discussion of the merits and limitations of quantum plasma models

Abstract

Shielding effects in non-degenerate and degenerate plasmas are compared. A detailed derivation of the Wigner-Poisson system is provided for electrostatic quantum plasmas where relativistic, spin and collisional effects are not essential. Later a detailed derivation of a quantum hydrodynamic model starting from the Wigner-Poisson system is shown. The route for this derivation considers the eikonal decomposition of the one-body wavefunctions of the quantum statistical mixture. The merits and limitations of the resulting quantum hydrodynamic model are discussed.