{
  "id": "math-ph/0508048",
  "version": "v1",
  "published": "2005-08-24T13:22:04.000Z",
  "updated": "2005-08-24T13:22:04.000Z",
  "title": "On the Convergence to a Statistical Equilibrium for the Dirac Equation",
  "authors": [
    "T. V. Dudnikova",
    "A. I. Komech",
    "N. J. Mauser"
  ],
  "comment": "12 pages",
  "journal": "Russian J. Math. Physics, 10 (2003), no.4, 399-410",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Dirac equation in $\\R^3$ with constant coefficients and study the distribution $\\mu_t$ of the random solution at time $t\\in\\R$. It is assumed that the initial measure $\\mu_0$ has zero mean, a translation-invariant covariance, and finite mean charge density. We also assume that $\\mu_0$ satisfies a mixing condition of Rosenblatt- or Ibragimov-Linnik-type. The main result is the convergence of $\\mu_t$ to a Gaussian measure as $t\\to\\infty$. The proof uses the study of long time asymptotics of the solution and S.N. Bernstein's ``room-corridor'' method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-24T13:22:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac equation",
      "statistical equilibrium",
      "convergence",
      "finite mean charge density",
      "long time asymptotics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...8048D"
    }
  }
}