We consider the quantum dynamics of N interacting fermions in the large N limit. The particles in the system interact with each other via repulsive interaction that is regularized Coulomb potential with a polynomial cutoff with respect to N. From the quantum system, we derive the Vlasov–Poisson system by simultaneously estimating the semiclassical and mean-field residues in terms of the Husimi measure.

中文翻译：

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从 N-费米子薛定谔方程向 Vlasov-Poisson 方程收敛

我们考虑大N极限下N 个相互作用费米子的量子动力学。系统中的粒子通过排斥相互作用彼此相互作用，排斥相互作用是正则化的库仑势，具有关于N的多项式截止。从量子系统中，我们通过根据 Husimi 测度同时估计半经典和平均场残差来推导出 Vlasov-Poisson 系统。