dorsal/arxiv
View SchemaSub-Planck spots of Schroedinger cats and quantum decoherence
| Authors | Wojciech Hubert Zurek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201118 |
| URL | https://arxiv.org/abs/quant-ph/0201118 |
| DOI | 10.1038/35089017 |
| Journal | Nature 412, 712-717 (2001) |
Abstract
Heisenberg's principle$^1$ states that the product of uncertainties of position and momentum should be no less than Planck's constant $\hbar$. This is usually taken to imply that phase space structures associated with sub-Planck ($\ll \hbar$) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schr\"odinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' $A \gg \hbar$ develop spotty structure on scales corresponding to sub-Planck $a = \hbar^2 / A \ll \hbar$. Such structures arise especially quickly in quantum versions of classically chaotic systems (such as gases, modelled by chaotic scattering of molecules), that are driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum manifestations of the exponential sensitivity to perturbations$^2$. Most importantly, these sub-Planck scales are physically significant: $a$ determines sensitivity of a quantum system (or of a quantum environment) to perturbations. Therefore sub-Planck $a$ controls the effectiveness of decoherence and einselection caused by the environment$^{3-8}$. It may also be relevant in setting limits on sensitivity of Schr\"odinger cats used as detectors.
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"abstract": "Heisenberg\u0027s principle$^1$ states that the product of uncertainties of\nposition and momentum should be no less than Planck\u0027s constant $\\hbar$. This is\nusually taken to imply that phase space structures associated with sub-Planck\n($\\ll \\hbar$) scales do not exist, or, at the very least, that they do not\nmatter. I show that this deeply ingrained prejudice is false: Non-local\n\"Schr\\\"odinger cat\" states of quantum systems confined to phase space volume\ncharacterized by `the classical action\u0027 $A \\gg \\hbar$ develop spotty structure\non scales corresponding to sub-Planck $a = \\hbar^2 / A \\ll \\hbar$. Such\nstructures arise especially quickly in quantum versions of classically chaotic\nsystems (such as gases, modelled by chaotic scattering of molecules), that are\ndriven into nonlocal Schr\\\"odinger cat -- like superpositions by the quantum\nmanifestations of the exponential sensitivity to perturbations$^2$. Most\nimportantly, these sub-Planck scales are physically significant: $a$ determines\nsensitivity of a quantum system (or of a quantum environment) to perturbations.\nTherefore sub-Planck $a$ controls the effectiveness of decoherence and\neinselection caused by the environment$^{3-8}$. It may also be relevant in\nsetting limits on sensitivity of Schr\\\"odinger cats used as detectors.",
"arxiv_id": "quant-ph/0201118",
"authors": [
"Wojciech Hubert Zurek"
],
"categories": [
"quant-ph"
],
"doi": "10.1038/35089017",
"journal_ref": "Nature 412, 712-717 (2001)",
"title": "Sub-Planck spots of Schroedinger cats and quantum decoherence",
"url": "https://arxiv.org/abs/quant-ph/0201118"
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