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

Laflèche, Laurent and Saffirio, Chiara. (2021) Strong semiclassical limit from Hartree and Hartree-Fock to Vlasov-Poisson equation. Preprints Fachbereich Mathematik, 2021 (04).

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Abstract

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. Our results hold for general initial data in some Sobolev space and are global in time.
Faculties and Departments:12 Special Collections > Preprints Fachbereich Mathematik
05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Kinetische Theorie (Saffirio)
UniBasel Contributors:Saffirio, Chiara
Item Type:Preprint
Publisher:Universität Basel
Language:English
edoc DOI:
Last Modified:01 Feb 2021 19:34
Deposited On:01 Feb 2021 19:34

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