Mean Field Asymptotics of Generalized Quantum Kinetic Equation

TL;DR

This paper rigorously derives the quantum Vlasov kinetic equation as the mean field limit of a generalized quantum kinetic equation, including cases with initial particle correlations.

Contribution

It provides a rigorous mathematical construction of the mean field asymptotics for the generalized quantum kinetic equation, extending to correlated initial states.

Findings

Quantum Vlasov equation derived as mean field limit

Method handles initial correlations between particles

Provides explicit unctionals for solution analysis

Abstract

We construct the mean field asymptotics of a solution of initial-value problem of the generalized quantum kinetic equation and a sequence of explicitly defined unctionals of a solution of stated kinetic equation. As a result the quantum Vlasov kinetic equation is rigorously derived. Moreover, in case of the presence of correlations of particles at initial time the mean field limit of a solution of the generalized quantum kinetic equation is constructed.