dorsal/arxiv
View SchemaCommuting Position and Momentum Operators, Exact Decoherence and Emergent Classicality
| Authors | J. J. Halliwell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507136 |
| URL | https://arxiv.org/abs/quant-ph/0507136 |
| DOI | 10.1103/PhysRevA.72.042109 |
| Journal | Phys Rev A 72, 042109 (2005) |
Abstract
Inspired by an old idea of von Neumann, we seek a pair of commuting operators X,P which are, in a specific sense, "close" to the canonical non-commuting position and momentum operators, x,p. The construction of such operators is related to the problem of finding complete sets of orthonormal phase space localized states, a problem severely constrained by the Balian-Low theorem. Here these constraints are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space). Commuting position and momentum operators are argued to be of use in discussions of emergent classicality from quantum mechanics. In particular, they may be used to give a discussion of the relationship between exact and approximate decoherence in the decoherent histories approach to quantum theory.
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"abstract": "Inspired by an old idea of von Neumann, we seek a pair of commuting operators\nX,P which are, in a specific sense, \"close\" to the canonical non-commuting\nposition and momentum operators, x,p. The construction of such operators is\nrelated to the problem of finding complete sets of orthonormal phase space\nlocalized states, a problem severely constrained by the Balian-Low theorem.\nHere these constraints are avoided by restricting attention to situations in\nwhich the density matrix is reasonably decohered (i.e., spread out in phase\nspace). Commuting position and momentum operators are argued to be of use in\ndiscussions of emergent classicality from quantum mechanics. In particular,\nthey may be used to give a discussion of the relationship between exact and\napproximate decoherence in the decoherent histories approach to quantum theory.",
"arxiv_id": "quant-ph/0507136",
"authors": [
"J. J. Halliwell"
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"quant-ph"
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"doi": "10.1103/PhysRevA.72.042109",
"journal_ref": "Phys Rev A 72, 042109 (2005)",
"title": "Commuting Position and Momentum Operators, Exact Decoherence and Emergent Classicality",
"url": "https://arxiv.org/abs/quant-ph/0507136"
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