{
  "id": "1004.2415",
  "version": "v2",
  "published": "2010-04-14T15:09:07.000Z",
  "updated": "2010-07-09T16:54:03.000Z",
  "title": "Products of random matrices and generalised quantum point scatterers",
  "authors": [
    "Alain Comtet",
    "Christophe Texier",
    "Yves Tourigny"
  ],
  "comment": "38 pages, 13 pdf figures. V2 : conclusion added ; Definition of function $\\Omega$ changed",
  "journal": "J. Stat. Phys. 140(3), 427-466 (2010)",
  "doi": "10.1007/s10955-010-0005-x",
  "categories": [
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "To every product of $2\\times2$ matrices, there corresponds a one-dimensional Schr\\\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\\em random} matrices are obtained by making these interactions and their positions random. We exhibit a simple one-dimensional quantum model corresponding to the most general product of matrices in $\\text{SL}(2, {\\mathbb R})$. We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-09T16:54:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalised quantum point scatterers",
      "random matrices",
      "simple one-dimensional quantum model corresponding",
      "potential consists"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2010,
      "month": "Aug",
      "volume": 140,
      "number": 3,
      "pages": 427
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JSP...140..427C"
    }
  }
}