Hurst Jérôme, Hervieux Paul-Antoine, Manfredi Giovanni
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, 67000 Strasbourg, France.
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, 67000 Strasbourg, France
Philos Trans A Math Phys Eng Sci. 2017 Apr 28;375(2092). doi: 10.1098/rsta.2016.0199.
Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-[Formula: see text] fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.
利用量子力学的相空间表述，我们推导了一个由自旋 - [公式：见原文] 费米子（通常为电子）组成的系统的四分量维格纳方程，其中包括塞曼效应和自旋 - 轨道耦合。这个维格纳方程与适当的麦克斯韦方程组耦合，以形成一个自洽的平均场模型。通过将完整的量子模型在普朗克常数下展开到一阶，得到了一组具有自旋效应的半经典弗拉索夫方程。通过取相空间分布函数的速度矩来推导相应的流体动力学方程。提出了一个简单的封闭关系以获得一组封闭的流体动力学方程。本文是主题为“气相、凝聚相和界面处非平衡和非统计动力学的理论与计算研究”特刊的一部分。
