{
  "id": "math-ph/0508053",
  "version": "v1",
  "published": "2005-08-26T15:47:11.000Z",
  "updated": "2005-08-26T15:47:11.000Z",
  "title": "On the Convergence to a Statistical Equilibrium in the Crystal Coupled to a Scalar Field",
  "authors": [
    "T. V. Dudnikova",
    "A. I. Komech"
  ],
  "comment": "33 pages",
  "journal": "Russ. J. Math. Physics, 12 (2005), no. 3, 301-325",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider the dynamics of a field coupled to a harmonic crystal with $n$ components in dimension $d$, $d,n\\ge 1$. The crystal and the dynamics are translation-invariant with respect to the subgroup $\\Z^d$ of $\\R^d$. The initial data is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. Moreover, initial correlation functions are translation-invariant with respect to the discrete subgroup $\\Z^d$. We study the distribution $\\mu_t$ of the solution at time $t\\in\\R$. The main result is the convergence of $\\mu_t$ to a Gaussian measure as $t\\to\\infty$, where $\\mu_\\infty$ is translation-invariant with respect to the subgroup $\\Z^d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-26T15:47:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scalar field",
      "statistical equilibrium",
      "convergence",
      "finite mean density"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...8053D"
    }
  }
}