dorsal/arxiv
View SchemaThe Quantum Mechanics of Hyperion
| Authors | Nathan Wiebe, L. E. Ballentine |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503170 |
| URL | https://arxiv.org/abs/quant-ph/0503170 |
| DOI | 10.1103/PhysRevA.72.022109 |
Abstract
This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.
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"abstract": "This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76,\n186 (1998)] that the chaotic tumbling of the satellite Hyperion would become\nnon-classical within 20 years, but for the effects of environmental\ndecoherence. The dynamics of quantum and classical probability distributions\nare compared for a satellite rotating perpendicular to its orbital plane,\ndriven by the gravitational gradient. The model is studied with and without\nenvironmental decoherence. Without decoherence, the maximum quantum-classical\n(QC) differences in its average angular momentum scale as hbar^{2/3} for\nchaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC\ndifferences for a macroscopic object like Hyperion. The quantum probability\ndistributions do not approach their classical limit smoothly, having an\nextremely fine oscillatory structure superimposed on the smooth classical\nbackground. For a macroscopic object, this oscillatory structure is too fine to\nbe resolved by any realistic measurement. Either a small amount of smoothing\n(due to the finite resolution of the apparatus) or a very small amount of\nenvironmental decoherence is sufficient ensure the classical limit. Under\ndecoherence, the QC differences in the probability distributions scale as\n(hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that\ndecoherence is not essential to explain the classical behavior of macroscopic\nbodies.",
"arxiv_id": "quant-ph/0503170",
"authors": [
"Nathan Wiebe",
"L. E. Ballentine"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.022109",
"title": "The Quantum Mechanics of Hyperion",
"url": "https://arxiv.org/abs/quant-ph/0503170"
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