{
  "id": "0711.1091",
  "version": "v1",
  "published": "2007-11-07T14:11:58.000Z",
  "updated": "2007-11-07T14:11:58.000Z",
  "title": "Convergence to equilibrium distribution. The Klein-Gordon equation coupled to a particle",
  "authors": [
    "T. V. Dudnikova"
  ],
  "comment": "22 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Hamiltonian system consisting of a Klein-Gordon vector field and a particle in $\\R^3$. The initial date of the system is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or Ibragimov-type mixing condition. Moreover, initial correlation functions are translation-invariant. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-07T14:11:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L15",
      "60Fxx",
      "60Gxx",
      "82Bxx"
    ],
    "keywords": [
      "klein-gordon equation",
      "equilibrium distribution",
      "convergence",
      "klein-gordon vector field",
      "finite mean density"
    ],
    "publication": {
      "doi": "10.1134/S1061920810010073",
      "journal": "Russian Journal of Mathematical Physics",
      "year": 2010,
      "month": "Mar",
      "volume": 17,
      "number": 1,
      "pages": 77
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010RJMP...17...77D"
    }
  }
}