dorsal/arxiv
View Schema$2\delta$-Kicked Quantum Rotors: Localization and `Critical' Statistics
| Authors | C. E. Creffield, G. Hur, T. S. Monteiro |
|---|---|
| Categories | |
| ArXiv ID | physics/0504074 |
| URL | https://arxiv.org/abs/physics/0504074 |
| DOI | 10.1103/PhysRevLett.96.024103 |
| Journal | Phys. Rev. Lett. 96, 024103 (2006). |
Abstract
The quantum dynamics of atoms subjected to pairs of closely-spaced $\delta$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation $\Sigma_2(L) \simeq \chi L \approx {1/2}(1-\nu) L$, where $\nu \approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent is analyzed.
{
"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
}