dorsal/arxiv
View SchemaCharacteristics of Quantum-Classical Correspondence for Two Interacting Spins
| Authors | J. Emerson, L. E. Ballentine |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011020 |
| URL | https://arxiv.org/abs/quant-ph/0011020 |
| DOI | 10.1103/PhysRevA.63.052103 |
| Journal | Phys. Rev. A 63, 052103 (2001); Erratum in PRA 64, 029901 (2001). |
Abstract
The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics well beyond the short-time regime of narrow states. We find that quantum-classical differences initially grow exponentially with a characteristic exponent consistently larger than the largest Lyapunov exponent. We provide numerical evidence that the time of the break between the quantum and classical predictions scales as log(${\cal J}/ \hbar$), where ${\cal J}$ is a characteristic system action. However, this log break-time rule applies only while the quantum-classical deviations are smaller than order hbar. We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.
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"abstract": "The conditions of quantum-classical correspondence for a system of two\ninteracting spins are investigated. Differences between quantum expectation\nvalues and classical Liouville averages are examined for both regular and\nchaotic dynamics well beyond the short-time regime of narrow states. We find\nthat quantum-classical differences initially grow exponentially with a\ncharacteristic exponent consistently larger than the largest Lyapunov exponent.\nWe provide numerical evidence that the time of the break between the quantum\nand classical predictions scales as log(${\\cal J}/ \\hbar$), where ${\\cal J}$ is\na characteristic system action. However, this log break-time rule applies only\nwhile the quantum-classical deviations are smaller than order hbar. We find\nthat the quantum observables remain well approximated by classical Liouville\naverages over long times even for the chaotic motions of a few\ndegree-of-freedom system. To obtain this correspondence it is not necessary to\nintroduce the decoherence effects of a many degree-of-freedom environment.",
"arxiv_id": "quant-ph/0011020",
"authors": [
"J. Emerson",
"L. E. Ballentine"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.63.052103",
"journal_ref": "Phys. Rev. A 63, 052103 (2001); Erratum in PRA 64, 029901 (2001).",
"title": "Characteristics of Quantum-Classical Correspondence for Two Interacting Spins",
"url": "https://arxiv.org/abs/quant-ph/0011020"
},
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