Mean-Field and Classical Limit for the N-Body Quantum Dynamics with Coulomb Interaction
Analysis of PDEs
2019-12-17 v1 Mathematical Physics
math.MP
Abstract
This paper proves the validity of the joint mean-field and classical limit of the quantum -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]].
Keywords
Cite
@article{arxiv.1912.06750,
title = {Mean-Field and Classical Limit for the N-Body Quantum Dynamics with Coulomb Interaction},
author = {François Golse and Thierry Paul},
journal= {arXiv preprint arXiv:1912.06750},
year = {2019}
}
Comments
35 pages, no figure