MEAN-FIELD AND CLASSICAL LIMIT FOR THE N-BODY QUANTUM DYNAMICS WITH COULOMB INTERACTION - École polytechnique Access content directly
Journal Articles Communications on Pure and Applied Mathematics Year : 2022

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

Abstract

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]].
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Dates and versions

hal-02361050 , version 1 (13-11-2019)
hal-02361050 , version 2 (09-12-2019)

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François Golse, Thierry Paul. MEAN-FIELD AND CLASSICAL LIMIT FOR THE N-BODY QUANTUM DYNAMICS WITH COULOMB INTERACTION. Communications on Pure and Applied Mathematics, 2022, ⟨10.1002/cpa.21986⟩. ⟨hal-02361050v2⟩
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