2017/07/14 by Klaus Renziehausen, Ingo Barth, Renziehausen, Klaus +1
Physics and Astronomy · #Dust and Plasma Wave Phenomena #FOS: Physical sciences #Ionosphere and magnetosphere dynamics #Nonlinear Waves and Solitons #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1707.04474
52 pages; Improvements in second version: Refs. [50] - [55] were added. In addition, among other, minor improvements, we decided to rename the many-particle Bohmian equations of motion into many-particle quantum Cauchy equations of motion because this renaming simplifies the interpretation of these equations
openalex publication_date 2017/07/14 · arxiv created 2017/11/16 · arxiv updated 2017/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.