{
  "id": "math-ph/0503056",
  "version": "v1",
  "published": "2005-03-23T17:32:33.000Z",
  "updated": "2005-03-23T17:32:33.000Z",
  "title": "Ordering of Energy Levels in Heisenberg Models and Applications",
  "authors": [
    "Bruno Nachtergaele",
    "Shannon Starr"
  ],
  "comment": "20 pages, contribution for the proceedings of QMATH9, Giens, September 2004",
  "journal": "in J. Ash and A. Joye (Eds), Mathematical Physics of Quantum Mechanics, Selected and Refereed Lectures from QMath9, Lecture Notes in Physics 690, Springer Verlag, 2006, pp 149--170",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture for the Heisenberg model with arbitrary spins and coupling constants on a chain. In this paper we give a pedagogical introduction to this result and also discuss some extensions and implications. The latter include the property that the relaxation time of symmetric simple exclusion processes on a graph for which FOEL can be proved, equals the relaxation time of a random walk on the same graph. This equality of relaxation times is known as Aldous' Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-23T17:32:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B10",
      "82B20"
    ],
    "keywords": [
      "energy levels",
      "relaxation time",
      "applications",
      "symmetric simple exclusion processes",
      "conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/3-540-34273-7_13",
      "journal": "Lecture Notes in Physics, Berlin Springer Verlag",
      "year": 2006,
      "volume": 690,
      "pages": 149
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006LNP...690..149N"
    }
  }
}