Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

TL;DR

This paper derives fluid moment hierarchy equations for quantum plasmas from gauge invariant quantum kinetic theory, ensuring consistency and providing a method to close the equations for practical use.

Contribution

It introduces a gauge invariant approach to derive quantum fluid equations from the Wigner function, addressing inconsistencies in gauge dependent formulations.

Findings

Linear transverse wave propagation matches kinetic theory in long wavelength limit

A closure method for the fluid equations is proposed

Gauge invariance ensures physical consistency of the model

Abstract

The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner function is shown to produce inconsistencies, if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and shown to be in agreement with the kinetic theory in the long wavelength approximation, provided an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.