{
  "id": "1204.3023",
  "version": "v5",
  "published": "2012-04-13T15:08:15.000Z",
  "updated": "2013-06-11T07:37:45.000Z",
  "title": "Extremal spacings between eigenphases of random unitary matrices and their tensor products",
  "authors": [
    "Marek Smaczynski",
    "Tomasz Tkocz",
    "Marek Kus",
    "Karol Zyczkowski"
  ],
  "journal": "Phys. Rev. E 88, 052902 (2013)",
  "doi": "10.1103/PhysRevE.88.052902",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.CD",
    "quant-ph"
  ],
  "abstract": "Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations from the Poissonian behavior.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-06-11T07:37:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.45.Pq",
      "02.70.-c",
      "11.55.-m"
    ],
    "keywords": [
      "random unitary matrices",
      "extremal spacings",
      "tensor product",
      "eigenphases",
      "nearest neighbor distribution"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2013,
      "month": "Nov",
      "volume": 88,
      "number": 5,
      "pages": "052902"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvE..88e2902S"
    }
  }
}