{
  "id": "1109.2776",
  "version": "v2",
  "published": "2011-09-13T13:16:22.000Z",
  "updated": "2013-05-20T19:19:28.000Z",
  "title": "Tunneling of the Kawasaki dynamics at low temperatures in two dimensions",
  "authors": [
    "J. Beltrán",
    "C. Landim"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Consider a lattice gas evolving according to the conservative Kawasaki dynamics at inverse temperature $\\beta$ on a two dimensional torus $\\Lambda_L=\\{0,..., L-1\\}^2$ . We prove the tunneling behavior of the process among the states of minimal energy. More precisely, assume that there are $n^2\\ll L$ particles and that the initial state is the configuration in which all sites of the square $\\mb x + \\{0,..., n-1\\}^2$ are occupied. We show that in the time scale $e^{2\\beta}$ the process is close to a Markov process on $\\Lambda_L$ which jumps from any site $\\mb x$ to any other site $\\mb y\\not =\\mb x$ at a strictly positive rate which can be expressed in terms of the jump rates of simple random walks.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-20T19:19:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low temperatures",
      "dimensions",
      "simple random walks",
      "lattice gas",
      "conservative kawasaki dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2776B"
    }
  }
}