{
  "annotation_id": "9a5d573b-0795-4f5e-a994-e1a4c2c7ae51",
  "date_created": "2026-03-02T18:01:38.074000Z",
  "date_modified": "2026-03-02T18:01:38.074000Z",
  "file_hash": "23316c4105aebcdb5b72b3723c70f2a27f5a2fb6bb33a40f9417d03708054c1f",
  "private": false,
  "record": {
    "abstract": "We propose a general construction of wave functions of arbitrary prescribed\nfractal dimension, for a wide class of quantum problems, including the infinite\npotential well, harmonic oscillator, linear potential and free particle. The\nbox-counting dimension of the probability density $P_t(x)=|\\Psi(x,t)|^2$ is\nshown not to change during the time evolution. We prove a universal relation\n$D_t=1+D_x/2$ linking the dimensions of space cross-sections $D_x$ and time\ncross-sections $D_t$ of the fractal quantum carpets.",
    "arxiv_id": "quant-ph/0005060",
    "authors": [
      "Daniel Wojcik",
      "Iwo Bialynicki-Birula",
      "Karol Zyczkowski"
    ],
    "categories": [
      "quant-ph",
      "nlin.CD"
    ],
    "doi": "10.1103/PhysRevLett.85.5022",
    "journal_ref": "Phys. Rev. Lett. 85, 5022 (2000)",
    "title": "Time Evolution of Quantum Fractals",
    "url": "https://arxiv.org/abs/quant-ph/0005060"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c977b048-9e54-4dff-a744-5dbd99501ad5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}