Version 1
: Received: 21 December 2018 / Approved: 24 December 2018 / Online: 24 December 2018 (15:24:11 CET)
How to cite:
Gerasimenko, V. Evolution of Correlations of Many-Particle Quantum Systems in Condensed States. Preprints2018, 2018120286. https://doi.org/10.20944/preprints201812.0286.v1
Gerasimenko, V. Evolution of Correlations of Many-Particle Quantum Systems in Condensed States. Preprints 2018, 2018120286. https://doi.org/10.20944/preprints201812.0286.v1
Gerasimenko, V. Evolution of Correlations of Many-Particle Quantum Systems in Condensed States. Preprints2018, 2018120286. https://doi.org/10.20944/preprints201812.0286.v1
APA Style
Gerasimenko, V. (2018). Evolution of Correlations of Many-Particle Quantum Systems in Condensed States. Preprints. https://doi.org/10.20944/preprints201812.0286.v1
Chicago/Turabian Style
Gerasimenko, V. 2018 "Evolution of Correlations of Many-Particle Quantum Systems in Condensed States" Preprints. https://doi.org/10.20944/preprints201812.0286.v1
Abstract
We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the de nition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.
Keywords
von Neumann hierarchy, nonlinear quantum BBGKY hierarchy, quantum kinetic equation, correlation of states, scaling limit.
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
