dorsal/arxiv
View SchemaThe Quantum-Classical Transition in Nonlinear Dynamical Systems
| Authors | Salman Habib, Kurt Jacobs, Hideo Mabuchi, Robert Ryne, Kosuke Shizume, Bala Sundaram |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0010093 |
| URL | https://arxiv.org/abs/quant-ph/0010093 |
| DOI | 10.1103/PhysRevLett.88.040402 |
| Journal | Phys. Rev. Lett. 88, 040402 (2002) |
Abstract
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.
{
"annotation_id": "4c6ca6ab-d974-403f-b796-9cfd2bc0d748",
"date_created": "2026-03-02T18:01:42.588000Z",
"date_modified": "2026-03-02T18:01:42.588000Z",
"file_hash": "465803e67e5ec7546df2596f452b4d047383d6311763700a0141f93ebd23c815",
"private": false,
"record": {
"abstract": "Viewed as approximations to quantum mechanics, classical evolutions can\nviolate the positive-semidefiniteness of the density matrix. The nature of this\nviolation suggests a classification of dynamical systems based on\nclassical-quantum correspondence; we show that this can be used to identify\nwhen environmental interaction (decoherence) will be unsuccessful in inducing\nthe quantum-classical transition. In particular, the late-time Wigner function\ncan become positive without any corresponding approach to classical dynamics.\nIn the light of these results, we emphasize key issues relevant for experiments\nstudying the quantum-classical transition.",
"arxiv_id": "quant-ph/0010093",
"authors": [
"Salman Habib",
"Kurt Jacobs",
"Hideo Mabuchi",
"Robert Ryne",
"Kosuke Shizume",
"Bala Sundaram"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.88.040402",
"journal_ref": "Phys. Rev. Lett. 88, 040402 (2002)",
"title": "The Quantum-Classical Transition in Nonlinear Dynamical Systems",
"url": "https://arxiv.org/abs/quant-ph/0010093"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "2399409a-d7fd-4cb6-8c75-e0ace3ea4380",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}