{
  "annotation_id": "167332f3-c540-4bf6-973a-ef7349605cde",
  "date_created": "2026-03-02T18:00:57.381000Z",
  "date_modified": "2026-03-02T18:00:57.381000Z",
  "file_hash": "e77399f04014937c7b47ec35c1ab5d8def5cf06a4f48729068be414d480d7f21",
  "private": false,
  "record": {
    "abstract": "The quantum dynamics of atoms subjected to pairs of closely-spaced\n$\\delta$-kicks from optical potentials are shown to be quite different from the\nwell-known paradigm of quantum chaos, the singly-$\\delta$-kicked system. We\nfind the unitary matrix has a new oscillating band structure corresponding to a\ncellular structure of phase-space and observe a spectral signature of a\nlocalization-delocalization transition from one cell to several. We find that\nthe eigenstates have localization lengths which scale with a fractional power\n$L \\sim \\hbar^{-.75}$ and obtain a regime of near-linear spectral variances\nwhich approximate the `critical statistics\u0027 relation $\\Sigma_2(L) \\simeq \\chi L\n\\approx {1/2}(1-\\nu) L$, where $\\nu \\approx 0.75$ is related to the fractal\nclassical phase-space structure. The origin of the $\\nu \\approx 0.75$ exponent\nis analyzed.",
    "arxiv_id": "physics/0504074",
    "authors": [
      "C. E. Creffield",
      "G. Hur",
      "T. S. Monteiro"
    ],
    "categories": [
      "physics.atom-ph",
      "cond-mat.other",
      "nlin.CD",
      "physics.gen-ph"
    ],
    "doi": "10.1103/PhysRevLett.96.024103",
    "journal_ref": "Phys. Rev. Lett. 96, 024103 (2006).",
    "title": "$2\\delta$-Kicked Quantum Rotors: Localization and `Critical\u0027 Statistics",
    "url": "https://arxiv.org/abs/physics/0504074"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "01dbef3a-8273-46f2-8b2b-b6c74c9ed25e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}