MEAN-FIELD AND CLASSICAL LIMIT FOR THE N-BODY QUANTUM DYNAMICS WITH COULOMB INTERACTION

François Golse (1) , Thierry Paul (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

This paper proves the validity of the joint mean-field and classical limit of the quantum N-body dynamics leading to the pressureless Euler-Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure. The interaction potential is assumed to be the repulsive Coulomb potential. The validity of this derivation is limited to finite time intervals on which the Euler-Poisson system has a smooth solution that is rapidly decaying at infinity. One key ingredient in the proof is an inequality from [S. Serfaty, with an appendix of M. Duerinckx arXiv:1803.08345v3 [math.AP]].

Mots clés: Quantum dynamics; Coulomb potential; Euler-Poisson system; Hartree equation; Mean-field limit; Semiclassical approximation

Domaines: Equations aux dérivées partielles [math.AP]

François Golse, Thierry Paul. MEAN-FIELD AND CLASSICAL LIMIT FOR THE N-BODY QUANTUM DYNAMICS WITH COULOMB INTERACTION. 2019. ⟨hal-02361050v1⟩