{
  "id": "1206.5748",
  "version": "v1",
  "published": "2012-06-25T17:55:35.000Z",
  "updated": "2012-06-25T17:55:35.000Z",
  "title": "The origin of order in random matrices with symmetries",
  "authors": [
    "Calvin W. Johnson"
  ],
  "comment": "5 figures; contribution to \"Beauty in Physics\" conference in honor of Francesco Iachello, May 2012, Cocoyoc, Mexico",
  "categories": [
    "math-ph",
    "math.MP",
    "nucl-th"
  ],
  "abstract": "From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with `low' quantum numbers and symmetric, low-dimensional irreps, but there is no \\textit{a priori} reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J=0 g.s. even for random two-body interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-25T17:55:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state",
      "quantum numbers",
      "nontrivial point-group symmetries",
      "extremal low-dimensional irreps",
      "random two-body interactions"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4759388"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1119623,
      "adsabs": "2012AIPC.1488..101J"
    }
  }
}