Mean-Field and Classical Limit for the N-Body Quantum Dynamics with Coulomb Interaction

被引：8

作者：

Golse, Francois ^{[1
]}

Paul, Thierry ^{[2
,3
]}

机构：

[1] Ecole Polytech, CMLS, Route Saclay, F-91128 Palaiseau, France

[2] Sorbonne Univ, CNRS, BC 187,4 Pl Jussieu, F-75252 Paris 05, France

[3] Sorbonne Univ, Lab JL Lions, BC 187,4 Pl Jussieu, F-75252 Paris 05, France

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2022年 / 75卷 / 06期

关键词：

SCHRODINGER-EQUATION; EMPIRICAL MEASURES; VLASOV EQUATIONS; APPROXIMATION; DERIVATION; SYSTEMS;

D O I：

10.1002/cpa.21986

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proves the validity of the joint mean-field and classical limit of the bosonic 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 taken from S. Serfaty (Duke Math. J. 169 (2020), 2887-2935) ).(c) 2021 Wiley Periodicals LLC.

引用

页码：1332 / 1376

页数：45

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