{
  "id": "math-ph/0508044",
  "version": "v1",
  "published": "2005-08-22T13:54:50.000Z",
  "updated": "2005-08-22T13:54:50.000Z",
  "title": "On a Two-Temperature Problem for Wave Equation",
  "authors": [
    "T. V. Dudnikova",
    "A. I. Komech",
    "H. Spohn"
  ],
  "comment": "30 pages",
  "journal": "Markov Processes and Related Fields 8 (2002), no.1, 43-80",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "Consider the wave equation with constant or variable coefficients in $\\R^3$. The initial datum is a random function with a finite mean density of energy that also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as $x_3\\to\\pm\\infty$, with the distributions $\\mu_\\pm$. We study the distribution $\\mu_t$ of the random solution at a time $t\\in\\R$. The main result is the convergence of $\\mu_t$ to a Gaussian translation-invariant measure as $t\\to\\infty$ that means central limit theorem for the wave equation. The proof is based on the Bernstein `room-corridor' argument. The application to the case of the Gibbs measures $\\mu_\\pm=g_\\pm$ with two different temperatures $T_{\\pm}$ is given. Limiting mean energy current density formally is $-\\infty\\cdot (0,0,T_+ -T_-)$ for the Gibbs measures, and it is finite and equals to $-C(0,0,T_+ -T_-)$ with $C>0$ for the convolution with a nontrivial test function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-22T13:54:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Fxx",
      "60Gxx",
      "82-xx"
    ],
    "keywords": [
      "wave equation",
      "two-temperature problem",
      "random function",
      "limiting mean energy current density",
      "gibbs measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...8044D"
    }
  }
}