{
  "id": "cond-mat/9712147",
  "version": "v1",
  "published": "1997-12-15T18:32:58.000Z",
  "updated": "1997-12-15T18:32:58.000Z",
  "title": "Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems",
  "authors": [
    "C. Basu",
    "C. M. Canali",
    "V. E. Kravtsov",
    "I. V. Yurkevich"
  ],
  "comment": "34 pages (RevTeX), 8 figures (postscript)",
  "doi": "10.1103/PhysRevB.57.14174",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric sigma-model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for T-breaking perturbations caused by a constant vector-potential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasi-localized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In $2d$ systems the distribution function $P(K)$ has a branching point at K=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent $d_{2}$ is suggested. Evidence of the branch-cut singularity is found in numerical simulations in $2d$ systems and at the Anderson transition point in $3d$ systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-12-15T18:32:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disordered systems",
      "level curvature distribution function",
      "eigenfunctions",
      "anderson transition point",
      "t-breaking perturbations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}