{
  "id": "quant-ph/0005060",
  "version": "v2",
  "published": "2000-05-16T14:32:26.000Z",
  "updated": "2000-09-20T10:58:10.000Z",
  "title": "Time Evolution of Quantum Fractals",
  "authors": [
    "Daniel Wojcik",
    "Iwo Bialynicki-Birula",
    "Karol Zyczkowski"
  ],
  "comment": "4 pages, 8 figures",
  "journal": "Phys. Rev. Lett. 85, 5022 (2000)",
  "doi": "10.1103/PhysRevLett.85.5022",
  "categories": [
    "quant-ph",
    "nlin.CD"
  ],
  "abstract": "We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential and free particle. The box-counting dimension of the probability density $P_t(x)=|\\Psi(x,t)|^2$ is shown not to change during the time evolution. We prove a universal relation $D_t=1+D_x/2$ linking the dimensions of space cross-sections $D_x$ and time cross-sections $D_t$ of the fractal quantum carpets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-09-20T10:58:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time evolution",
      "quantum fractals",
      "fractal quantum carpets",
      "arbitrary prescribed fractal dimension",
      "wave functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}