This paper proves the validity of the joint mean-field and classical limit of the bosonic quantum N-body dynamics leading to the pressureless Euler-Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure. The interaction potential is assumed to be the repulsive Coulomb potential. The validity of this derivation is limited to finite time intervals on which the Euler-Poisson system has a smooth solution that is rapidly decaying at infinity. One key ingredient in the proof is an inequality taken from S. Serfaty (Duke Math. J. 169 (2020), 2887–2935) ).© 2021 Wiley Periodicals LLC.

中文翻译：

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库仑相互作用 N 体量子动力学的平均场和经典极限

本文证明了导致无压欧拉-泊松系统的玻色子量子N体动力学的联合平均场和经典极限的有效性，用于分解初始数据，其第一个边际具有单动 Wigner 测度。假设相互作用势是排斥的库仑势。此推导的有效性仅限于有限时间间隔，在该有限时间间隔内，欧拉-泊松系统具有在无穷大处快速衰减的平滑解。证明中的一个关键要素是取自 S. Serfaty 的不等式（Duke Math. J. 169 (2020), 2887–2935)）。© 2021 Wiley Periodicals LLC。