{
  "id": "cond-mat/9804023",
  "version": "v1",
  "published": "1998-04-03T08:27:16.000Z",
  "updated": "1998-04-03T08:27:16.000Z",
  "title": "Universal singularity at the closure of a gap in a random matrix theory",
  "authors": [
    "E. Brezin",
    "S. Hikami"
  ],
  "comment": "20pages, Revtex, to be published in Phys. Rev. E",
  "doi": "10.1103/PhysRevE.57.4140",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider a Hamiltonian $ H = H_0+ V $, in which $ H_0$ is a given non-random Hermitian matrix,and $V$ is an $N \\times N$ Hermitian random matrix with a Gaussian probability distribution.We had shown before that Dyson's universality of the short-range correlations between energy levels holds at generic points of the spectrum independently of $H_{0}$. We consider here the case in which the spectrum of $H_{0}$ is such that there is a gap in the average density of eigenvalues of $H$ which is thus split into two pieces. When the spectrum of $H_{0}$ is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-04-03T08:27:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix theory",
      "universal singularity",
      "hermitian random matrix",
      "gaussian probability distribution",
      "non-random hermitian matrix"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}