SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5533-5553, January 2020.
We study the semiclassical limit from the time-dependent Hartree equation with Coulomb or gravitational potential to the Vlasov--Poisson equation. We prove convergence in trace norm for mixed states under a technical assumption on the solution of the Vlasov--Poisson equation. We exhibit a special class of mixed quasi-free states which satisfy this assumption.

中文翻译：

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从Hartree方程到Vlasov-Poisson系统：一类混合状态的强收敛

SIAM数学分析杂志，第52卷，第6期，第5533-5553页，2020年1月。
我们研究了从具有库仑或引力的时变Hartree方程到Vlasov-Poisson方程的半经典极限。我们在Vlasov-Poisson方程解的技术假设下证明了混合态的迹范数的收敛性。我们展示了满足这一假设的一类特殊的混合准自由状态。