BBGKY Hierarchy and Dynamics of Correlations

TL;DR

This paper derives the BBGKY hierarchy for quantum many-particle systems, providing a framework to analyze their dynamics through correlation operators and constructing solutions for systems with n-body interactions.

Contribution

It introduces a derivation of the BBGKY hierarchy for Fermi and Bose systems using the von Neumann hierarchy, and constructs solutions for n-body interaction potentials.

Findings

Established the BBGKY hierarchy for quantum systems.

Constructed solutions in the space of trace-class operators.

Provided a framework for analyzing many-particle quantum dynamics.

Abstract

We derive the BBGKY hierarchy for the Fermi and Bose many-particle systems, using the von Neumann hierarchy for the correlation operators. The solution of the Cauchy problem of the formulated hierarchy for the case of a n-body interaction potential is constructed in the space of sequences of trace-class operators.