{
  "annotation_id": "7688ac23-9b4b-4153-b557-5516e6d5036c",
  "date_created": "2026-03-02T18:01:46.131000Z",
  "date_modified": "2026-03-02T18:01:46.131000Z",
  "file_hash": "18cb0591c889da6ea1f7080f9bf544f69621a1396caef7a298dac1a353752323",
  "private": false,
  "record": {
    "abstract": "Physical fractals invariably have upper and lower limits for their fractal\nstructure. Berry has shown that a particle sharply confined to a box has a wave\nfunction that is fractal both in time and space, with no lower limit. In this\narticle, two idealizations of this picture are softened and a corresponding\nlower bound for fractality obtained. For a box created by repeated measurements\n(\\`a la the quantum Zeno effect), the lower bound is $\\Delta x\\sim \\Delta t\n(\\hbar/{mL})$ with $\\Dt$ the interval between measurements and $L$ is the size\nof the box. For a relativistic particle, the lower bound is the Compton\nwavelength, $\\hbar/mc$. The key step in deriving both results is to write the\npropagator as a sum over classical paths.",
    "arxiv_id": "quant-ph/0109149",
    "authors": [
      "L. S. Schulman"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0960-0779(02)00027-9",
    "journal_ref": "Chaos, Solitons \u0026 Fractals 14, 823-830 (2002)",
    "title": "Limits of fractality: Zeno boxes and relativistic particles",
    "url": "https://arxiv.org/abs/quant-ph/0109149"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0e27ec6e-5fba-46a2-ad35-d9f6d5ee3af9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}