{
  "id": "1111.4735",
  "version": "v2",
  "published": "2011-11-21T05:23:25.000Z",
  "updated": "2013-03-06T05:18:22.000Z",
  "title": "Rate of Convergence Towards Semi-Relativistic Hartree Dynamics",
  "authors": [
    "Ji Oon Lee"
  ],
  "comment": "29 pages",
  "journal": "Ann. Henri Poincar\\'e 14 (2013), 313-346",
  "doi": "10.1007/s00023-012-0188-6",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the semi-relativistic system of $N$ gravitating Bosons with gravitation constant $G$. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where $N \\to \\infty$ and $G \\to 0$ while $GN = \\lambda$ fixed. In the super-critical regime of large $\\lambda$, we introduce the regularized interaction where the cutoff vanishes as $N \\to \\infty$. We show that the difference between the many-body semi-relativistic Schr\\\"{o}dinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order $N^{-1}$ for all $\\lambda$, i.e., the result covers the sub-critical regime and the super-critical regime. The $N$ dependence of the bound is optimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-06T05:18:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "82C10",
      "35Q55"
    ],
    "keywords": [
      "convergence",
      "relativistic dispersion law",
      "super-critical regime",
      "corresponding semi-relativistic hartree dynamics",
      "semi-relativistic system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4735O"
    }
  }
}