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

Abstract

AbstractThis 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) ).© 2021 Wiley Periodicals LLC.