Eur. Phys. J. D (2014) 68: 176
https://doi.org/10.1140/epjd/e2014-50205-5

Regular Article

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

Institut de Physique et Chimie des Matériaux de Strasbourg and Labex NIE, Université de Strasbourg, CNRS UMR 7504, BP 43, 67034 Strasbourg Cedex 2, France

^a e-mail: Giovanni.Manfredi@ipcms.unistra.fr

Received: 13 March 2014
Received in final form: 14 April 2014
Published online: 27 June 2014

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.