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

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 repulsi...

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Bibliographic Details
Published inCommunications on pure and applied mathematics Vol. 75; no. 6; pp. 1332 - 1376
Main Authors Golse, François, Paul, Thierry
Format Journal Article
LanguageEnglish
Published Melbourne John Wiley & Sons Australia, Ltd 01.06.2022
John Wiley and Sons, Limited
Wiley
Subjects
Analysis of PDEs
Coulomb potential
Mathematics
Hartree equation
Euler-Poisson system
Coulomb potential
Quantum dynamics
Semiclassical approximation
Mean-field limit
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Summary: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) ).© 2021 Wiley Periodicals LLC.
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ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21986