{
  "id": "cond-mat/0401179",
  "version": "v1",
  "published": "2004-01-12T19:09:05.000Z",
  "updated": "2004-01-12T19:09:05.000Z",
  "title": "Vlasov stability of the Hamiltonian Mean Field model",
  "authors": [
    "Celia Anteneodo",
    "Raul O. Vallejos"
  ],
  "comment": "11 pages, 5 figures. Submitted as a contribution to the proceedings of the International Workshop on Trends and Perspectives on Extensive and Non-Extensive Statistical Mechanics, November, 19-21, 2003, Angra dos Reis, Brazil",
  "doi": "10.1016/j.physa.2004.06.006",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the dynamical stability of a fully-coupled system of $N$ inertial rotators, the so-called Hamiltonian Mean Field model. In the limit $N \\to \\infty$, and after proper scaling of the interactions, the $\\mu$-space dynamics is governed by a Vlasov equation. We apply a nonlinear stability test to (i) a selected set of spatially homogeneous solutions of Vlasov equation, qualitatively similar to those observed in the quasi-stationary states arising from fully magnetized initial conditions, and (ii) numerical coarse-grained distributions of the finite-$N$ dynamics. Our results are consistent with previous numerical evidence of the disappearance of the homogenous quasi-stationary family below a certain energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-12T19:09:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian mean field model",
      "vlasov stability",
      "vlasov equation",
      "nonlinear stability test",
      "fully magnetized initial conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}