# Strong semiclassical limit from Hartree and Hartree-Fock to Vlasov-Poisson equation

@article{Lafleche2020StrongSL, title={Strong semiclassical limit from Hartree and Hartree-Fock to Vlasov-Poisson equation}, author={Laurent Lafleche and Chiara Saffirio}, journal={arXiv: Mathematical Physics}, year={2020} }

In this paper we consider the semiclassical limit from the Hartree to the Vlasov equation with general singular interaction potential including the Coulomb and gravitational interactions, and we prove explicit bounds in the strong topologies of Schatten norms. Moreover, in the case of Fermions, we provide estimates on the size of the exchange term in the Hartree-Fock equation and also obtain a rate of convergence for the semiclassical limit from Hartree-Fock to Vlasov equation in Schatten norms…

## 13 Citations

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We investigate the semiclassical limit from the semi-relativistic Hartree-Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relativistic dispersion…

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