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

Jérôme Hurst; Omar Morandi; Giovanni Manfredi; Paul-Antoine Hervieux

doi:10.1140/epjd/e2014-50205-5

EPJ

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

Jérôme Hurst, Omar Morandi, Giovanni Manfredi^a and Paul-Antoine Hervieux

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

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.

Contribution to the Topical Issue “Theory and Applications of the Vlasov Equation”, edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.

23rd International Summer School on Vacuum, Electron, and Ion Technologies (VEIT)
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EPJ

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

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