{
  "id": "cond-mat/0403220",
  "version": "v1",
  "published": "2004-03-08T18:52:37.000Z",
  "updated": "2004-03-08T18:52:37.000Z",
  "title": "Vicious Walkers in a Potential",
  "authors": [
    "Alan J. Bray",
    "Karen Winkler"
  ],
  "comment": "5 pages",
  "journal": "J. Phys. A 37, 5493 (2004)",
  "doi": "10.1088/0305-4470/37/21/001",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider N vicious walkers moving in one dimension in a one-body potential v(x). Using the backward Fokker-Planck equation we derive exact results for the asymptotic form of the survival probability Q(x,t) of vicious walkers initially located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential. Explicit results are given for a square-well potential with absorbing or reflecting boundary conditions at the walls, and for a harmonic potential with an absorbing or reflecting boundary at the origin and the walkers starting on the positive half line. By mapping the problem of N vicious walkers in zero potential onto the harmonic potential problem, we rederive the results of Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A 33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a semi-infinite line with an absorbing wall at the origin. This mapping also gives a new result for vicious walkers on a semi-infinite line with a reflecting boundary at the origin: Q(x,t) \\sim t^{-N(N-1)/2}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-08T18:52:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vicious walkers",
      "semi-infinite line",
      "harmonic potential problem",
      "survival probability",
      "arbitrary attractive potential"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}