考虑自旋轨道相互作用的量子漂移-扩散方程的形式推导
Formal derivation of quantum drift-diffusion equations with spin-orbit interaction
摘要：
本文从碰撞Wigner方程出发，导出了具有Rashba型自旋-轨道相互作用的二维电子气的量子漂移-扩散方程。碰撞模型的Bhatnagar-Gross-Krook型运营商描述的电子气的放松到局部平衡，这是由量子最大熵原则。由于算子的非交换性，标准的扩散标度不能用于这方面，需要流体动力学时间标度。一个Chapman-Enskog程序导致，直到一阶的弛豫时间，系统的非局域量子漂移扩散方程的电荷密度和自旋矢量密度。局部方程，包括玻姆势得到的半经典扩展到二阶标度普朗克常数。这项工作的主要新颖之处是，所有的自旋分量被认为是，而以前的模型只考虑特殊的自旋方向。
英文摘要：
Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interactions of Rashba type are formally derived from a collisional Wigner equation. The collisions are modeled by a Bhatnagar-Gross-Krook-type operator describing the relaxation of the electron gas to a local equilibrium that is given by the quantum maximum entropy principle. Because of non-commutativity properties of the operators, the standard diffusion scaling cannot be used in this context, and a hydrodynamic time scaling is required. A Chapman-Enskog procedure leads, up to first order in the relaxation time, to a system of nonlocal quantum drift-diffusion equations for the charge density and spin vector densities. Local equations including the Bohm potential are obtained in the semiclassical expansion up to second order in the scaled Planck constant. The main novelty of this work is that all spin components are considered, while previous models only consider special spin directions.
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