{
  "id": "2105.14270",
  "version": "v1",
  "published": "2021-05-29T11:09:54.000Z",
  "updated": "2021-05-29T11:09:54.000Z",
  "title": "A discontinuity of the energy of quantum walk in impurities",
  "authors": [
    "Kenta Higuchi",
    "Takashi Komatsu",
    "Norio Konno",
    "Hisashi Morioka",
    "Etsuo Segawa"
  ],
  "comment": "16 pages. arXiv admin note: text overlap with arXiv:1912.11555",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the discrete-time quantum walk whose local dynamics is denoted by $C$ at the perturbed region $\\{0,1,\\dots,M-1\\}$ and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow $\\omega^n$ at time $n$ $(|\\omega|=1)$. From this expression, we compute the scattering on the surface of $-1$ and $M$ and also compute the quantity how quantum walker accumulates in the perturbed region; namely the energy of the quantum walk, in the long time limit. We find a discontinuity of the energy with respect to the frequency of the inflow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-29T11:09:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discontinuity",
      "impurities",
      "discrete-time quantum walk",
      "quantum walker accumulates",
      "long time limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}