Renziehausen, K., Barth, I.

Many-particle quantum hydrodynamics: Exact equations and pressure tensors
Progress of Theoretical and Experimental Physics **2018**, (1),pp 013A05/1-44 (2018)
In the first part of this paper, the many-particle quantum hydrodynamics equations for a system
containing many particles of different sorts are derived exactly from the many-particle
Schrödinger equation, including the derivation of the many-particle continuity equations, many-particle Ehrenfest equations of motion, and many-particle quantum Cauchy equations 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 the many-particle
quantum Cauchy equations, there appears a quantity called the 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 the
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.

TH-2018-02