Quantum kinetic theories in degenerate plasmas

TL;DR

This review explores quantum kinetic theories for degenerate plasmas, emphasizing Fermi surface dynamics, wave-particle interactions, and exchange effects, providing new models and insights into wave damping and dispersion relations.

Contribution

It introduces a Fermi surface-based model for degenerate plasmas and compares exchange corrections to traditional density functional theory approaches.

Findings

Fermi surface deformation remains small even at large amplitudes.

New wave damping mechanisms due to multi-quantum absorption/emission.

Exchange corrections vary in accuracy between Langmuir and ion-acoustic waves.

Abstract

In this review we give an overview of recent work on quantum kinetic theories of plasmas. We focus, in particular, on the case where the electrons are fully degenerate. For such systems, perturbation methods using the distribution function can be problematic. Instead we present a model that considers the dynamics of the Fermi surface. The advantage of this model is that, even though the value of the distribution function can be greatly perturbed outside the equilibrium Fermi surface, deformation of Fermi surface is small up very large amplitudes. Next, we investigate the short-scale dynamics for which the Wigner-Moyal equation replaces the Vlasov equation. In particular, we study wave-particle interaction, and deduce that new types of wave damping can occur due to the simultaneous absorption (or emission) of multiple wave quanta. Finally, we consider exchange effects within a quantum kinetic formalism to find a model more accurate than ones using exchange potentials from density functional theory. We deduce the exchange corrections to the dispersion relations for Langmuir and ion-acoustic waves. Comparing with results based on exchange potentials deduced from density functional theory we find that the latter models are reasonably accurate for Langmuir waves, but rather inaccurate for ion acoustic waves.