{
  "id": "1204.0125",
  "version": "v3",
  "published": "2012-03-31T19:38:11.000Z",
  "updated": "2013-04-23T16:25:30.000Z",
  "title": "On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A Quadratic Trap",
  "authors": [
    "Xuwen Chen"
  ],
  "comment": "Revised according to the referee report. Accepted to appear in Archive for Rational Mechanics and Analysis",
  "journal": "Archive for Rational Mechanics and Analysis, Vol. 210 (2013), 365-408",
  "doi": "10.1007/s00205-013-0645-5",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider the dynamics of the 3D N-body Schr\\\"{o}dinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N^{3{\\beta}-1}V(N^{{\\beta}}x). We justify the mean-field approximation and offer a rigorous derivation of the 3D cubic NLS with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon [30] for {\\beta} in (0,2/7] by adapting and simplifying an argument in Chen and Pavlovi\\'c [7] which solves the problem for {\\beta} in (0,1/4) in the absence of a trap.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-23T16:25:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A02",
      "81V70",
      "35A23",
      "35B45",
      "81Q05"
    ],
    "keywords": [
      "3d cubic nonlinear schrödinger equation",
      "quadratic trap",
      "rigorous derivation",
      "3d cubic nls",
      "pair interaction potential"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2013,
      "month": "Nov",
      "volume": 210,
      "number": 2,
      "pages": 365
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013ArRMA.210..365C"
    }
  }
}