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.
Semiclassical Vlasov and fluid models for an electron gas with spin effects / Hurst, Jérôme; Morandi, Omar; Manfredi, Giovanni; Hervieux, Paul-Antoine. - In: THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR AND OPTICAL PHYSICS. - ISSN 1434-6060. - STAMPA. - 68:(2014), pp. 176-186. [10.1140/epjd/e2014-50205-5]
Semiclassical Vlasov and fluid models for an electron gas with spin effects
MORANDI, OMAR;
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.File | Dimensione | Formato | |
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