dorsal/arxiv
View SchemaApproximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory
| Authors | J. J. Halliwell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011103 |
| URL | https://arxiv.org/abs/quant-ph/0011103 |
| DOI | 10.1103/PhysRevD.63.085013 |
| Journal | Phys.Rev. D63 (2001) 085013 |
Abstract
This paper explores the possibility that an exactly decoherent set of histories may be constructed from an approximately decoherent set by small distortions of the operators characterizing the histories. In particular, for the case of histories of positions and momenta, this is achieved by doubling the set of operators and then finding, amongst this enlarged set, new position and momentum operators which commute, so decohere exactly, and which are ``close'' to the original operators. The enlarged, exactly decoherent, theory has the same classical dynamics as the original one, and coincides with the so-called deterministic quantum theories of the type recently studied by 't Hooft. These results suggest that the comparison of standard and deterministic quantum theories may provide an alternative method of characterizing emergent classicality. A side-product is the surprising result that histories of momenta in the quantum Brownian motion model (for the free particle in the high-temperature limit) are exactly decoherent.
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"abstract": "This paper explores the possibility that an exactly decoherent set of\nhistories may be constructed from an approximately decoherent set by small\ndistortions of the operators characterizing the histories. In particular, for\nthe case of histories of positions and momenta, this is achieved by doubling\nthe set of operators and then finding, amongst this enlarged set, new position\nand momentum operators which commute, so decohere exactly, and which are\n``close\u0027\u0027 to the original operators. The enlarged, exactly decoherent, theory\nhas the same classical dynamics as the original one, and coincides with the\nso-called deterministic quantum theories of the type recently studied by \u0027t\nHooft. These results suggest that the comparison of standard and deterministic\nquantum theories may provide an alternative method of characterizing emergent\nclassicality. A side-product is the surprising result that histories of momenta\nin the quantum Brownian motion model (for the free particle in the\nhigh-temperature limit) are exactly decoherent.",
"arxiv_id": "quant-ph/0011103",
"authors": [
"J. J. Halliwell"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevD.63.085013",
"journal_ref": "Phys.Rev. D63 (2001) 085013",
"title": "Approximate Decoherence of Histories and \u0027t Hooft\u0027s Deterministic Quantum Theory",
"url": "https://arxiv.org/abs/quant-ph/0011103"
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