The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems
Abstract
The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the -particle statistical operators, which are solutions of the BBGKY hierarchy, and with the -particle correlation operators of quantum systems.
Cite
@article{arxiv.0712.4336,
title = {The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems},
author = {V. I. Gerasimenko and V. O. Shtyk},
journal= {arXiv preprint arXiv:0712.4336},
year = {2010}
}
Comments
26 pages