{
  "id": "cond-mat/9809175",
  "version": "v1",
  "published": "1998-09-11T15:42:22.000Z",
  "updated": "1998-09-11T15:42:22.000Z",
  "title": "Self-Diffusion in Simple Models: Systems with Long-Range Jumps",
  "authors": [
    "A. Asselah",
    "R. Brito",
    "J. L. Lebowitz"
  ],
  "comment": "24 pages, in TeX, 1 figure, e-mail addresses: asselah@math.ethz.ch, brito@seneca.fis.ucm.es, lebowitz@math.rutgers.edu",
  "journal": "Journal of Statistical Physics 87 (1997) 1131--1144",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self diffusion coefficient, $D_N(\\rho)$, in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set of $N$ neighboring sites. We obtain positive upper and lower bounds on $F_N(\\rho)=N((1-\\r)-[D_N(\\rho)/D_N(0)])/(\\rho(1-\\rho))$ for $\\rho\\in [0,1]$. Computer simulations for the square, triangular and one dimensional lattice suggest that $F_N$ becomes effectively independent of $N$ for $N\\ge 20$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-11T15:42:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple models",
      "long-range jumps",
      "self-diffusion",
      "simple symmetric exclusion",
      "self diffusion coefficient"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}