{
  "id": "1205.4689",
  "version": "v2",
  "published": "2012-05-21T18:58:07.000Z",
  "updated": "2013-11-03T09:03:48.000Z",
  "title": "Birth and death processes and quantum spin chains",
  "authors": [
    "Alberto F. Grünbaum",
    "Luc Vinet",
    "Alexei Zhedanov"
  ],
  "comment": "14 pages",
  "journal": "J. Math. Phys. 54, 062101 (2013)",
  "categories": [
    "quant-ph"
  ],
  "abstract": "This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that transition amplitudes between single excitation states of the spin chains have an expression in terms of orthogonal polynomials which is analogous to the Karlin-McGregor representation formula of the transition probability functions for classes of birth and death processes. As an application, we present a characterization of spin systems for which the probability to return to the point of origin at some time is 1 or almost 1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-03T09:03:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ta",
      "02.50.Cw"
    ],
    "keywords": [
      "death processes",
      "quantum spin chains",
      "single excitation states",
      "transition probability functions",
      "spin chain hamiltonians"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "doi": "10.1063/1.4808235",
      "year": 2013,
      "month": "Jun",
      "volume": 54,
      "number": 6,
      "pages": 2101
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JMP....54f2101G"
    }
  }
}