{
  "id": "cond-mat/0205572",
  "version": "v2",
  "published": "2002-05-27T19:31:15.000Z",
  "updated": "2002-11-08T19:46:41.000Z",
  "title": "Failure of single-parameter scaling of wave functions in Anderson localization",
  "authors": [
    "S. L. A. de Queiroz"
  ],
  "comment": "RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published)",
  "journal": "Physical Review B 66, 195113 (2002)",
  "doi": "10.1103/PhysRevB.66.195113",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \\times \\infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $ L \\leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \\lesssim -S \\lesssim 0.30$ for the range of parameters used in our study, .",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-08T19:46:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anderson localization",
      "wave functions",
      "single-parameter scaling",
      "wavefunction amplitude distributions result",
      "reproduce exact diagonalization results"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}