dorsal/arxiv
View SchemaSub-Planck Structure, Decoherence, and Many-Body Environments
| Authors | Andrew Jordan, Mark Srednicki |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112139 |
| URL | https://arxiv.org/abs/quant-ph/0112139 |
Abstract
In a recent paper [Nature 412, 712 (2001)], Zurek has argued that (1) time evolution typically causes chaotic quantum systems to generate structure that varies on the scale of phase-space volume elements of size $(\hbar^2/A)^d$, where A is a classical action characteristic of the state and d is the number of degrees of freedom, and that (2) this structure implies that a small change in a phase-space coordinate X by an amount $\delta X \sim \hbar X/A$ generically results in an orthogonal state. While we agree with (1), we argue that (2) is not correct if the number of degrees of freedom is small. Our arguments are based on the Berry-Voros ansatz for the structure of energy eigenstates in chaotic systems. We find, however, that (2) becomes valid if the number of degrees of freedom is large. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence.
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"abstract": "In a recent paper [Nature 412, 712 (2001)], Zurek has argued that (1) time\nevolution typically causes chaotic quantum systems to generate structure that\nvaries on the scale of phase-space volume elements of size $(\\hbar^2/A)^d$,\nwhere A is a classical action characteristic of the state and d is the number\nof degrees of freedom, and that (2) this structure implies that a small change\nin a phase-space coordinate X by an amount $\\delta X \\sim \\hbar X/A$\ngenerically results in an orthogonal state. While we agree with (1), we argue\nthat (2) is not correct if the number of degrees of freedom is small. Our\narguments are based on the Berry-Voros ansatz for the structure of energy\neigenstates in chaotic systems. We find, however, that (2) becomes valid if the\nnumber of degrees of freedom is large. This implies that many-body environments\nmay be crucial for the phenomenon of quantum decoherence.",
"arxiv_id": "quant-ph/0112139",
"authors": [
"Andrew Jordan",
"Mark Srednicki"
],
"categories": [
"quant-ph"
],
"title": "Sub-Planck Structure, Decoherence, and Many-Body Environments",
"url": "https://arxiv.org/abs/quant-ph/0112139"
},
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