{
  "id": "0812.2740",
  "version": "v2",
  "published": "2008-12-15T08:10:47.000Z",
  "updated": "2010-05-02T03:23:38.000Z",
  "title": "The quintic NLS as the mean field limit of a Boson gas with three-body interactions",
  "authors": [
    "Thomas Chen",
    "Nataša Pavlović"
  ],
  "comment": "AMS Latex, 35 pages",
  "journal": "Journal of Functional Analysis, 260 (4), 959 - 997, 2011",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We investigate the dynamics of a boson gas with three-body interactions in dimensions $d=1,2$. We prove that in the limit of infinite particle number, the BBGKY hierarchy of $k$-particle marginals converges to a limiting (Gross-Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness of solutions. Factorized solutions of the GP hierarchy are shown to be determined by solutions of a quintic nonlinear Schr\\\"odinger equation. Our proof is based on, and extends, methods of Erd\\\"os-Schlein-Yau, Klainerman-Machedon, and Kirkpatrick-Schlein-Staffilani.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-02T03:23:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "81V70"
    ],
    "keywords": [
      "mean field limit",
      "boson gas",
      "three-body interactions",
      "quintic nls",
      "infinite particle number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2740C"
    }
  }
}