# From the Hartree dynamics to the Vlasov equation

Benedikter, Niels; Porta, Marcello; Saffirio, Chiara; Schlein, Benjamin (2016). From the Hartree dynamics to the Vlasov equation. Archiv for Rational Mechanics and Analysis, 221(1):273-334.

## Abstract

We consider the evolution of quasi-free states describing $\mathit{N}$ fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large $\mathit{N}$, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise bounds on the 0rate of convergence.

## Abstract

We consider the evolution of quasi-free states describing $\mathit{N}$ fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large $\mathit{N}$, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise bounds on the 0rate of convergence.

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