{
  "id": "2304.06464",
  "version": "v1",
  "published": "2023-04-13T13:02:20.000Z",
  "updated": "2023-04-13T13:02:20.000Z",
  "title": "Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian",
  "authors": [
    "Takuya Machida"
  ],
  "comment": "15 pages, 5 figures",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "Focusing on a continuous-time quantum walk on $\\mathbb{Z}=\\left\\{0,\\pm 1,\\pm 2,\\ldots\\right\\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and its system is operated by a spatially periodic Hamiltonian. As a result, we see an asymmetry probability distribution. To catch a long-time behavior, we also try to find a long-time limit theorem and realize that the limit distribution holds a symmetry density function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-13T13:02:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous-time quantum walk",
      "asymmetry probability distribution",
      "long-time limit theorem",
      "limit distribution holds",
      "symmetry density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}