Derivation of Dirac Exchange Interaction Potential from Quantum Plasma Kinetic Theory

TL;DR

This paper derives the Dirac exchange interaction potential from quantum kinetic theory for collisionless plasmas, providing a new perspective on its role in quantum plasma modeling and density functional theory.

Contribution

It introduces a derivation of the Dirac exchange potential from quantum kinetic equations, applicable to degenerate electron gases and plasma systems, expanding theoretical understanding.

Findings

Correlation potential energy is smaller than exchange contribution.

Macroscopic hydrodynamic equations include the Dirac exchange term.

A simplified form of the quantum plasma exchange kinetic theory is proposed.

Abstract

The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for real systems is worked out, in terms of temperature and density parameters. Within the region of applicability, the correlation potential energy is shown to be always smaller than the exchange contribution. From the moments of the quantum kinetic equations, macroscopic, hydrodynamic equations are found, for an electron-ion plasma. The Dirac exchange term is explicitly derived, in the case of a completely degenerate electron gas. These results show, within quantum kinetic theory for charged particle systems, a new view of the Dirac exchange interaction frequently used in density functional theory parametrization. Finally, a simpler form of the quantum plasma exchange kinetic theory is also found.