{
  "id": "1307.7017",
  "version": "v1",
  "published": "2013-07-26T12:37:56.000Z",
  "updated": "2013-07-26T12:37:56.000Z",
  "title": "An averaging theorem for FPU in the thermodynamic limit",
  "authors": [
    "Alberto Maiocchi",
    "Dario Bambusi",
    "Andrea Carati"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Consider an FPU chain composed of $N\\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\\beta^{-1}$. Given a fixed $K<N$, we construct $K$ packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order $\\beta^{1-a}$, $a>0$) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $\\beta$. The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\\to\\infty$, $\\beta>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-26T12:37:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermodynamic limit",
      "averaging theorem",
      "time autocorrelation function",
      "adiabatic invariants",
      "fpu chain"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-014-0958-2",
      "journal": "Journal of Statistical Physics",
      "year": 2014,
      "month": "Apr",
      "volume": 155,
      "number": 2,
      "pages": 300
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JSP...155..300M"
    }
  }
}