{
  "id": "1205.5116",
  "version": "v1",
  "published": "2012-05-23T07:50:33.000Z",
  "updated": "2012-05-23T07:50:33.000Z",
  "title": "Weak subordination breaking for the quenched trap model",
  "authors": [
    "Stas Burov",
    "Eli Barkai"
  ],
  "comment": "15 pages. 7 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We map the problem of diffusion in the quenched trap model onto a new stochastic process: Brownian motion which is terminated at the coverage \"time\" ${\\cal S}_\\alpha=\\sum_{x=-\\infty} ^\\infty (n_x)^\\alpha$ with $n_x$ being the number of visits to site $x$. Here $0<\\alpha=T/T_g<1$ is a measure of the disorder in the original model. This mapping allows us to treat the intricate correlations in the underlying random walk in the random environment. The operational \"time\" ${\\cal S}_\\alpha$ is changed to laboratory time $t$ with a L\\'evy time transformation. Investigation of Brownian motion stopped at \"time\" ${\\cal S}_\\alpha$ yields the diffusion front of the quenched trap model which is favorably compared with numerical simulations. In the zero temperature limit of $\\alpha\\to 0$ we recover the renormalization group solution obtained by C. Monthus. Our theory surmounts critical slowing down which is found when $\\alpha \\to 1$. Above the critical dimension two mapping the problem to a continuous time random walk becomes feasible though still not trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-23T07:50:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.Jc",
      "02.50.-r",
      "05.20.-y",
      "46.65.+g"
    ],
    "keywords": [
      "quenched trap model",
      "weak subordination breaking",
      "brownian motion",
      "levy time transformation",
      "continuous time random walk"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.86.041137",
      "journal": "Physical Review E",
      "year": 2012,
      "month": "Oct",
      "volume": 86,
      "number": 4,
      "pages": "041137"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhRvE..86d1137B"
    }
  }
}