arXiv:1912.06750 Abstract | arXiv Analytics

arXiv:1912.06750 [math.AP]Abstract References Reviews Resources

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

Published 2019-12-14Version 1

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]].

Comments: 35 pages, no figure

Categories: math.AP, math-ph, math.MP

Subjects: 82C10, 35Q41, 35Q55, 35Q83, 82C05

Keywords: n-body quantum dynamics, classical limit, coulomb interaction, monokinetic wigner measure, finite time intervals

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