Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the Vlasov equation with singular interaction, including the Coulomb potential. To reach this objective, we also prove the propagation of velocity moments and weighted Schatten norms which implies the bound...

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Veröffentlicht in:Journal of statistical physics 2019-10, Vol.177 (1), p.20-60
1. Verfasser: Lafleche, Laurent
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Coulomb potential
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Norms
Physical Chemistry
Physics
Physics and Astronomy
Plancks constant
Propagation velocity
Quantum Physics
Space density
Statistical Physics and Dynamical Systems
Theoretical
Vlasov equations
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Beschreibung
Zusammenfassung:In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the Vlasov equation with singular interaction, including the Coulomb potential. To reach this objective, we also prove the propagation of velocity moments and weighted Schatten norms which implies the boundedness of the space density of particles uniformly in the Planck constant.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-019-02356-7