Semiclassical Vlasov and fluid models for an electron gas with spin effects

TL;DR

This paper develops a semiclassical model combining classical orbital motion with quantum spin effects for an electron gas, deriving Vlasov and hydrodynamic equations that incorporate quantum spin dynamics.

Contribution

It introduces a novel four-component Vlasov equation and corresponding hydrodynamic models that integrate quantum spin effects into classical electron gas descriptions.

Findings

Derived a four-component Vlasov equation for spin-1/2 fermions.

Formulated hydrodynamic equations using maximum entropy principles.

Applicable to both Maxwell-Boltzmann and Fermi-Dirac statistics.

Abstract

We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.