The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

Details The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

2007-12-28

arxiv.org/abs/0712.4336v2

J. Stat. Mech. (2008) P03007

Physics

Mathematical Physics

26 pages

Scientific paper

10.1088/1742-5468/2008/03/P03007

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 $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.

Affiliated with

Also associated with

No associations

Rating

The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-508280