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Strong semiclassical
limits from Hartree and Hartree–Fock to Vlasov–Poisson
equations
Laurent Lafleche and Chiara Saffirio |
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Vol. 16 (2023), No. 4, 891–926
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Abstract |
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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 the Hartree–Fock to the Vlasov equation in Schatten norms. Our results hold for general initial data in some Sobolev space and any fixed time interval. |
Keywords
Hartree equation, Hartree–Fock equation, Vlasov equation,
Coulomb interaction, gravitational interaction,
semiclassical limit
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Mathematical Subject Classification
Primary: 35Q41, 35Q55, 82C10
Secondary: 35Q83, 82C05
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Milestones
Received: 4 May 2020
Revised: 20 September 2021
Accepted: 19 October 2021
Published: 15 June 2023
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Authors |
| Laurent Lafleche | |
| Department of Mathematics The University of Texas at Austin Austin, TX United States |
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| Chiara Saffirio | |
| Department of Mathematics and
Computer Science University of Basel Basel Switzerland |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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