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

Understand

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.