{
  "id": "1004.3623",
  "version": "v2",
  "published": "2010-04-21T05:40:20.000Z",
  "updated": "2010-10-18T00:52:24.000Z",
  "title": "On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two",
  "authors": [
    "Luigi Accardi",
    "Farrukh Mukhamedov",
    "Mansoor Saburov"
  ],
  "comment": "19 pages",
  "journal": "Infinite Dim. Anal. Quantum Probab. Related Topics Vol. 14, No. 3 (2011) 443--463",
  "doi": "10.1142/S021902571100447X",
  "categories": [
    "math-ph",
    "math.DS",
    "math.FA",
    "math.MP"
  ],
  "abstract": "In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-18T00:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L53",
      "60J99",
      "46L60",
      "60G50",
      "82B10",
      "81Q10",
      "94A17"
    ],
    "keywords": [
      "cayley tree",
      "associated chain",
      "boundary conditions",
      "uniqueness",
      "study forward quantum markov chains"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 852772,
      "adsabs": "2010arXiv1004.3623A"
    }
  }
}