{
  "id": "1912.06750",
  "version": "v1",
  "published": "2019-12-14T00:07:19.000Z",
  "updated": "2019-12-14T00:07:19.000Z",
  "title": "Mean-Field and Classical Limit for the N-Body Quantum Dynamics with Coulomb Interaction",
  "authors": [
    "François Golse",
    "Thierry Paul"
  ],
  "comment": "35 pages, no figure",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "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]].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-14T00:07:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C10",
      "35Q41",
      "35Q55",
      "35Q83",
      "82C05"
    ],
    "keywords": [
      "n-body quantum dynamics",
      "classical limit",
      "coulomb interaction",
      "monokinetic wigner measure",
      "finite time intervals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}