On Dynamics of Correlations in Quantum Many-Particle Systems

TL;DR

This paper develops a rigorous, nonperturbative framework for describing the evolution of correlations in large quantum many-particle systems, including their creation, propagation, and mean field limits.

Contribution

It introduces a nonperturbative solution to the hierarchy of nonlinear evolution equations for correlation operators and an approach to describe correlation dynamics from one-particle states.

Findings

Constructed a nonperturbative solution for the correlation hierarchy.

Developed an approach to describe correlation creation and propagation.

Established the mean field asymptotic behavior of correlation operators.

Abstract

The paper deals with the problem of the rigorous description of the evolution of states of large particle quantum systems by means of correlation operators. A nonperturbative solution of the Cauchy problem of the hierarchy of nonlinear evolution equations for a sequence of marginal correlation operators is constructed. For initial states specified in terms of a one-particle density operator and correlation operators we also develop an approach to the description of the processes of the creation and the propagation of correlations within the framework of a one-particle density operator. Moreover, the mean field asymptotic behavior of constructed marginal correlation operators is established.