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

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.

To appear in the European Physical Journal D, Topical Issue "Theory and Applications of the Vlasov Equation"

References in corpus (4)

• Spin magnetohydrodynamics
• Breather mode in the many-electron dynamics of semiconductor quantum wells
• From extended phase space dynamics to fluid theory
• Lagrangian approach to the semi-relativistic electron dynamics in the mean-field approximation

Cited by in corpus (8)

• Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas
• Solid state plasmas
• Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma, Part I: Dielectric permeability tensor for magnetized plasmas
• Kinetic theory for spin-polarized relativistic plasmas
• Quantum kinetic theories in degenerate plasmas
• Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma, Part II: Dispersion dependencies
• Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions
• Ultrafast dynamics of a spin-polarized electron plasma with magnetic ions