Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

Autor: Laurent Lafleche
Přispěvatelé: CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre de Mathématiques Laurent Schwartz (CMLS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
Rok vydání: 2019
Předmět:
Équation de Vlasov
FOS: Physical sciences
Semiclassical physics
Space (mathematics)
Planck constant
01 natural sciences
010305 fluids & plasmas
symbols.namesake
Mathematics - Analysis of PDEs
Vlasov equation
Intéraction Coulombienne
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]
Semiclassical limit
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Velocity Moments
Hartree equation
0103 physical sciences
FOS: Mathematics
Nonlinear Schrödinger equation
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Limit (mathematics)
010306 general physics
Mathematical Physics
Mathematical physics
Physics
Quantum Physics
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Hartree
Équation de Hartree
16. Peace & justice
82C10
35Q41
35Q55
82C05
35Q83
Équation de Schrödinger nonlinéaire
Coulomb interaction
symbols
Gravitational interaction
Intéraction gravitationnelle
Electric potential
Limite semi-classique
Quantum Physics (quant-ph)
Analysis of PDEs (math.AP)
Zdroj: Journal of Statistical Physics. 177:20-60
ISSN: 1572-9613
0022-4715
DOI: 10.1007/s10955-019-02356-7
Popis: 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.
42 pages, typos added, clarifications of hypotheses in theorems 3 and 4 and missing sup_{[0,T]} added
Databáze: OpenAIRE
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