多粒子量子流体力学：精确方程和压力张量
Many-particle quantum hydrodynamics: exact equations and pressure tensors
摘要：
本文的第一部分从多粒子薛定谔方程出发，严格推导了含有多种粒子系统的多粒子量子流体力学（MPQHD）方程。它包括推导多粒子连续性方程（MPCE），多粒子运动方程（MPEEM）和多粒子量子柯西方程（MPQCE）的任何不同的粒子种类和总粒子系综。在我们的分析中的新的一点是，我们考虑一组任意的不同种类的粒子在系统中。在MPQCE中，出现了一个称为压力张量的量。在本文的第二部分，我们深入分析了这个张量的两个版本--Wyatt压力张量和Kuzmenkov压力张量。有不同的版本，因为压力张量有一个类似于势的规范自由度。我们发现，所有的量贡献的怀亚特压力张量的解释是可以理解的，但库兹曼科夫张量，这是困难的。此外，对于Wyatt张量，从笛卡尔坐标到柱坐标的转换可以以明确的方式完成，但对于Kuzmenkov张量，这是相当麻烦的。
英文摘要：
In the first part of this paper, the many-particle quantum hydrodynamics (MPQHD) equations for a system containing many particles of different sorts are derived exactly from the many-particle Schrödinger equation. It includes the derivation of the many-particle continuity equations (MPCE), many-particle Ehrenfest equations of motion (MPEEM), and many-particle quantum Cauchy equations (MPQCE) for any of the different particle sorts and for the total particle ensemble. The new point in our analysis is that we consider a set of arbitrary particles of different sorts in the system. In MPQCEs, there appears a quantity called pressure tensor. In the second part of this paper, we analyze two versions of this tensor in depth -- the Wyatt pressure tensor and the Kuzmenkov pressure tensor. There are different versions because there is a gauge freedom for the pressure tensor similar to that for potentials. We find that the interpretation of all quantities contributing to the Wyatt pressure tensor is understandable but for the Kuzmenkov tensor, it is difficult. Furthermore, the transformation from Cartesian coordinates to cylindrical coordinates for the Wyatt tensor can be done in a clear way, but for the Kuzmenkov tensor, it is rather cumbersome.
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