{
  "id": "0907.4313",
  "version": "v2",
  "published": "2009-07-24T15:33:11.000Z",
  "updated": "2009-12-10T16:51:31.000Z",
  "title": "Mean-Field Dynamics: Singular Potentials and Rate of Convergence",
  "authors": [
    "Antti Knowles",
    "Peter Pickl"
  ],
  "comment": "Typos corrected",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the time evolution of a system of $N$ identical bosons whose interaction potential is rescaled by $N^{-1}$. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state. It is well known that in the mean-field limit $N \\to \\infty$ the quantum $N$-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong, possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum $N$-body dynamics to the Hartree dynamics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-10T16:51:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C10",
      "35Q40",
      "35Q55",
      "82C21"
    ],
    "keywords": [
      "mean-field dynamics",
      "singular potentials",
      "convergence",
      "mean-field limit",
      "body dynamics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-010-1010-2",
      "journal": "Communications in Mathematical Physics",
      "year": 2010,
      "month": "Aug",
      "volume": 298,
      "number": 1,
      "pages": 101
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.298..101K"
    }
  }
}