On Evolution Equations for Marginal Correlation Operators

TL;DR

This paper derives a rigorous nonlinear quantum BBGKY hierarchy for marginal correlation operators in quantum many-particle systems and constructs a nonperturbative solution to its Cauchy problem.

Contribution

It introduces a novel derivation of the nonlinear quantum BBGKY hierarchy from the von Neumann hierarchy, offering an alternative to density operator methods.

Findings

Rigorous derivation of the nonlinear quantum BBGKY hierarchy

Construction of a nonperturbative solution to the hierarchy's Cauchy problem

Provides a new framework for describing nonequilibrium correlations in quantum systems

Abstract

This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann hierarchy for correlation operators that give an alternative approach to the description of states in comparison with the density operators. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed.