dorsal/arxiv
View SchemaArnol'd Tongues and Quantum Accelerator Modes
| Authors | Italo Guarneri, Laura Rebuzzini, Shmuel Fishman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512086 |
| URL | https://arxiv.org/abs/quant-ph/0512086 |
| DOI | 10.1088/0951-7715/19/5/006 |
| Journal | Nonlinearity 19 (2006) 1141-1164 |
Abstract
The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.
{
"annotation_id": "471ff64e-5c9b-4f74-a7d6-8928bbeef802",
"date_created": "2026-03-02T18:02:24.178000Z",
"date_modified": "2026-03-02T18:02:24.178000Z",
"file_hash": "7e1a9d39e1753e03f3a7ef04c59ca89dd2b79199a2aef7259243bd922b5f3162",
"private": false,
"record": {
"abstract": "The stable periodic orbits of an area-preserving map on the 2-torus, which is\nformally a variant of the Standard Map, have been shown to explain the quantum\naccelerator modes that were discovered in experiments with laser-cooled atoms.\nWe show that their parametric dependence exhibits Arnol\u0027d-like tongues and\nperform a perturbative analysis of such structures. We thus explain the\narithmetical organisation of the accelerator modes and discuss experimental\nimplications thereof.",
"arxiv_id": "quant-ph/0512086",
"authors": [
"Italo Guarneri",
"Laura Rebuzzini",
"Shmuel Fishman"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"nlin.CD"
],
"doi": "10.1088/0951-7715/19/5/006",
"journal_ref": "Nonlinearity 19 (2006) 1141-1164",
"title": "Arnol\u0027d Tongues and Quantum Accelerator Modes",
"url": "https://arxiv.org/abs/quant-ph/0512086"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "41f9da85-8392-4891-abdb-9f62b2d94569",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}