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Mean‐Field and Classical Limit for the N ‐Body Quantum Dynamics with Coulomb Interaction
- Source :
- Communications on Pure and Applied Mathematics. 75:1332-1376
- Publication Year :
- 2021
- Publisher :
- Wiley, 2021.
-
Abstract
- 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]].
- Subjects :
- Applied Mathematics
General Mathematics
Quantum dynamics
media_common.quotation_subject
010102 general mathematics
Infinity
01 natural sciences
Measure (mathematics)
Classical limit
010104 statistics & probability
Mean field theory
Coulomb
Electric potential
0101 mathematics
Quantum
Mathematical physics
media_common
Mathematics
Subjects
Details
- ISSN :
- 10970312 and 00103640
- Volume :
- 75
- Database :
- OpenAIRE
- Journal :
- Communications on Pure and Applied Mathematics
- Accession number :
- edsair.doi...........4e19c47b4733dc442aa002f4b318d476