等离子体的量子流体力学--一种新的量子流体力学理论
Quantum hydrodynamics for plasmas -- a Thomas-Fermi theory perspective
摘要：
在流体力学框架（量子流体力学，QHD）中描述量子系统的想法可以追溯到Madelung和Bohm。虽然这样的描述形式上对于单个粒子是精确的，但是最近Manfredi和Haas [Phys. Rev. B { \bf 64}，075316（2001）]将该概念应用于多粒子系统，并且在量子等离子体团体的部分中受到高度欢迎。因此，这些方程的适用性限制往往被忽略，从而产生非物理的预测。在这里，我们证明了修改后的QHD方程的等离子体可以来自包括梯度修正的Escheras-Fermi理论。这使QHD有了坚实的基础。同时，该推导在依赖于系统维数$D$的量子（玻姆）势之前产生不同的前因子$γ=(D-2/3D)$。我们的方法允许一个确定QHD的局限性，并概述系统的改进。
英文摘要：
The idea to describe quantum systems within a hydrodynamic framework (quantum hydrodynamics, QHD) goes back to Madelung and Bohm. While such a description is formally exact for a single particle, more recently the concept has been applied to many-particle systems by Manfredi and Haas [Phys. Rev. B {\bf 64}, 075316 (2001)] and received high popularity in parts of the quantum plasma community. Thereby, often the applicability limits of these equations are ignored, giving rise to unphysical predictions. Here we demonstrate that modified QHD equations for plasmas can be derived from Thomas-Fermi theory including gradient corrections. This puts QHD on firm grounds. At the same time this derivation yields a different prefactor, $γ=(D-2/3D)$, in front of the quantum (Bohm) potential which depends on the system dimensionality $D$. Our approach allows one to identify the limitations of QHD and to outline systematic improvements.
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