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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| Published in | Communications on pure and applied mathematics Vol. 75; no. 6; pp. 1332 - 1376 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Melbourne
John Wiley & Sons Australia, Ltd
01.06.2022
John Wiley and Sons, Limited Wiley |
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| Abstract | 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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| AbstractList | 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. 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. 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]]. |
| Author | Golse, François Paul, Thierry |
| Author_xml | – sequence: 1 givenname: François surname: Golse fullname: Golse, François email: francois.golse@polytechnique.edu organization: CMLS, École polytechnique, Route de Saclay – sequence: 2 givenname: Thierry surname: Paul fullname: Paul, Thierry email: paul@ljll.math.upmc.fr organization: CNRS & Laboratoire J.‐L. Lions, Sorbonne Université |
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| Keywords | Hartree equation Euler-Poisson system Coulomb potential Quantum dynamics Semiclassical approximation Mean-field limit |
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| Snippet | 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... 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... 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... |
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| SubjectTerms | Analysis of PDEs Coulomb potential Mathematics |
| Title | Mean‐Field and Classical Limit for the N‐Body Quantum Dynamics with Coulomb Interaction |
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