{
  "id": "0910.0111",
  "version": "v2",
  "published": "2009-10-01T09:00:48.000Z",
  "updated": "2010-02-01T08:49:04.000Z",
  "title": "Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach",
  "authors": [
    "Cecile Monthus",
    "Thomas Garel"
  ],
  "comment": "7 pages, 7 figures; v2=final version",
  "journal": "Phys. Rev. E 81, 011138 (2010)",
  "doi": "10.1103/PhysRevE.81.011138",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We consider the continuous-time random walk of a particle in a two-dimensional self-affine quenched random potential of Hurst exponent $H>0$. The corresponding master equation is studied via the strong disorder renormalization procedure introduced in Ref. [C. Monthus and T. Garel, J. Phys. A: Math. Theor. 41 (2008) 255002]. We present numerical results on the statistics of the equilibrium time $t_{eq}$ over the disordered samples of a given size $L \\times L$ for $10 \\leq L \\leq 80$. We find an 'Infinite disorder fixed point', where the equilibrium barrier $\\Gamma_{eq} \\equiv \\ln t_{eq}$ scales as $\\Gamma_{eq}=L^H u $ where $u$ is a random variable of order O(1). This corresponds to a logarithmically-slow diffusion $ | \\vec r(t) - \\vec r(0) | \\sim (\\ln t)^{1/H}$ for the position $\\vec r(t)$ of the particle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-01T08:49:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.-a",
      "05.45.Df",
      "05.60.-k"
    ],
    "keywords": [
      "two-dimensional self-affine random potentials",
      "strong disorder renormalization approach",
      "random walk",
      "self-affine quenched random potential"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2010,
      "month": "Jan",
      "volume": 81,
      "number": 1,
      "pages": "011138"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvE..81a1138M"
    }
  }
}