{
  "id": "cond-mat/0001086",
  "version": "v1",
  "published": "2000-01-08T18:22:30.000Z",
  "updated": "2000-01-08T18:22:30.000Z",
  "title": "Fluctuations of the inverse participation ratio at the Anderson transition",
  "authors": [
    "F. Evers",
    "A. D. Mirlin"
  ],
  "comment": "4 pages, 3 eps figures",
  "journal": "Phys. Rev. Lett. 84, 3690 (2000).",
  "doi": "10.1103/PhysRevLett.84.3690",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.dis-nn"
  ],
  "abstract": "Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant, with a power-law asymptotic ``tail''. This scale invariance implies that the fractal dimensions $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $\\chi$ is violated in the regime of strong multifractality, with $\\chi\\to 1$ in the limit $D_2\\to 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-01-08T18:22:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse participation ratio",
      "anderson transition",
      "fluctuations",
      "power-law random banded matrix model",
      "scale invariance implies"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}