{
  "id": "cond-mat/0211676",
  "version": "v2",
  "published": "2002-11-28T19:16:16.000Z",
  "updated": "2003-07-03T18:17:18.000Z",
  "title": "Description of Quantum Systems by Random Matrix Ensembles of High Dimensions",
  "authors": [
    "Maciej M. Duras"
  ],
  "comment": "3 pages; to appear in: \"Proceedings of ICSSUR'6, Sixth International Conference on Squeezed States and Uncertainty Relations, 24th May 1999 - 29th May 1999, Universita` degli Studi di Napoli 'Federico II', Naples, Italy\", NASA, Greenbelt, Maryland, USA (1999)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for $N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian unitary ensemble GUE($N$), $N$-dimensional Gaussian symplectic ensemble GSE($N$), and Poisson ensemble PE, is formulated: {\\it The probability density functions of the dimensionless second difference of the three adjacent energy levels take on maximum at the origin for the following ensembles: GOE($N$), GUE($N$), GSE($N$), and PE, where $N \\geq 3$.} The notions of {\\it level homogenization with level clustering} and {\\it level homogenization with level repulsion} are introduced.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-07-03T18:17:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix ensembles",
      "high dimensions",
      "quantum systems",
      "gaussian unitary ensemble gue",
      "gaussian orthogonal ensemble goe"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat.11676D"
    }
  }
}