On description of quantum plasma

TL;DR

This paper reviews the methods for describing quantum plasma, focusing on hydrodynamic and kinetic models, highlighting their assumptions, limitations, and fundamental problems needing further research.

Contribution

It provides a comprehensive analysis of existing quantum plasma models, clarifying their applicability and identifying key unresolved issues in the linear approximation.

Findings

Hydrodynamic description has specific applicability limits.

Linear dielectric response reveals fundamental problems in quantum plasma modeling.

Further investigation is needed for nonlinear and kinetic effects.

Abstract

A plasma becomes quantum when the quantum nature of its particles significantly affects its macroscopic properties. To answer the question of when the collective quantum plasma effects are important, a proper description of such effects is necessary. We consider here the most common methods of description of quantum plasma, along with the related assumptions and applicability limits. In particular, we analyze in detail the hydrodynamic description of quantum plasma, as well as discuss some kinetic features of analytic properties of linear dielectric response function in quantum plasma. We point out the most important, in our view, fundamental problems occurring already in the linear approximation and requiring further investigation. (submitted to Physics-Uspekhi)