{
  "id": "1412.1496",
  "version": "v1",
  "published": "2014-12-03T21:28:55.000Z",
  "updated": "2014-12-03T21:28:55.000Z",
  "title": "Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivities",
  "authors": [
    "David S. Dean",
    "Thomas Guérin"
  ],
  "comment": "8 pages, 2 figures, revtex",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity which is assumed to be periodic. When the system is asymptotically diffusive the mean squared displacement, characterizing the dispersion in the system, is, at late times, a linear function of time. A Kubo type formula is given for the mean squared displacement which allows the recovery of some known results for the effective diffusion constant $D_e$ in a direct way, but also allows an understanding of the asymptotic approach to the diffusive limit. In particular, as well as as computing the slope of a linear fit to the late time mean squared displacement, we find a formula for the constant where the fit intersects the y axis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-03T21:28:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.50.Ey",
      "05.10.Gg"
    ],
    "keywords": [
      "asymptotically diffusive behavior",
      "brownian particle",
      "diffusivity",
      "periodic diffusivities",
      "late time mean squared displacement"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.90.062114",
      "journal": "Physical Review E",
      "year": 2014,
      "month": "Dec",
      "volume": 90,
      "number": 6,
      "pages": "062114"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvE..90f2114D"
    }
  }
}