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In this paper, we prove a quantitative version of the semiclassical limitfrom the Hartree to the Vlasov equation with singular interaction, includingthe Coulomb potential. To reach this objective, we also prove the propagationof velocity moments and weighted Schatten norms which implies the boundednessof the space density of particles uniformly in the Planck constant.

Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation