{
  "id": "cond-mat/0203602",
  "version": "v1",
  "published": "2002-03-29T00:51:06.000Z",
  "updated": "2002-03-29T00:51:06.000Z",
  "title": "Fractional Dynamical Behavior in Quantum Brownian Motion",
  "authors": [
    "Kyungsik Kim",
    "Y. S. Kong",
    "M. K. Yum",
    "J. T. Kim"
  ],
  "comment": "9 pages, 3 figures, Latex",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The dynamical behavior for a quantum Brownian particle is investigated under a random potential of the fractional iterative map on a one-dimensional lattice. For our case, the quantum expectation values can be obtained numerically from the wave function of the fractional Schr$\\ddot{o}$dinger equation. Particularly, the square of mean displacement which is ensemble-averaged over our configuration is found to be proportional approximately to $t^{\\delta}$ in the long time limit, where $\\delta$ $=$ $0.96 \\pm 0.02$. The power-law behavior with scaling exponents $\\epsilon$ $=$ $0.98 \\pm 0.02$ and $\\theta$ $=$ $ 0.51 \\pm 0.01$ is estimated for $ \\bar {{< p(t) >}^2}$ and $ \\bar {{< f(t) >}^2}$, and the result presented is compared with other numerical calculations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-29T00:51:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum brownian motion",
      "fractional dynamical behavior",
      "quantum brownian particle",
      "long time limit",
      "quantum expectation values"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat..3602K"
    }
  }
}