Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations

TL;DR

This paper rigorously analyzes the kinetic evolution of large quantum particle systems with initial correlations, using mean field limits and marginal observables to describe their asymptotic behavior.

Contribution

It introduces two approaches for describing quantum many-particle evolution: one via marginal observables and another via a generalized quantum kinetic equation.

Findings

Derivation of mean field asymptotics for quantum systems with initial correlations

Development of a framework using marginal observables in the mean field limit

Formulation of a generalized quantum kinetic equation for initial correlated states

Abstract

In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems. One of the developed approaches consists in the description of the evolution of quantum many-particle systems within the framework of marginal observables in mean field scaling limit. Another method based on the possibility to describe the evolution of states within the framework of a one-particle marginal density operator governed by the generalized quantum kinetic equation in case of initial states specified by a one-particle marginal density operator and correlation operators.