dorsal/arxiv
View SchemaDecoherence of Hydrodynamic Histories: A Simple Spin Model
| Authors | T. A. Brun, J. J. Halliwell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9601004 |
| URL | https://arxiv.org/abs/quant-ph/9601004 |
| DOI | 10.1103/PhysRevD.54.2899 |
| Journal | Phys.Rev.D54:2899-2912,1996 |
Abstract
In the context of the decoherent histories approach to the quantum mechanics of closed systems, Gell-Mann and Hartle have argued that the variables typically characterizing the quasiclassical domain of a large complex system are the integrals over small volumes of locally conserved densities -- hydrodynamic variables. The aim of this paper is to exhibit some simple models in which approximate decoherence arises as a result of local conservation. We derive a formula which shows the explicit connection between local conservation and approximate decoherence. We then consider a class of models consisting of a large number of weakly interacting components, in which the projections onto local densities may be decomposed into projections onto one of two alternatives of the individual components. The main example we consider is a one-dimensional chain of locally coupled spins, and the projections are onto the total spin in a subsection of the chain. We compute the decoherence functional for histories of local densities, in the limit when the number of components is very large. We find that decoherence requires two things: the smearing volumes must be sufficiently large to ensure approximate conservation, and the local densities must be partitioned into sufficiently large ranges to ensure protection against quantum fluctuations.
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"abstract": "In the context of the decoherent histories approach to the quantum mechanics\nof closed systems, Gell-Mann and Hartle have argued that the variables\ntypically characterizing the quasiclassical domain of a large complex system\nare the integrals over small volumes of locally conserved densities --\nhydrodynamic variables. The aim of this paper is to exhibit some simple models\nin which approximate decoherence arises as a result of local conservation. We\nderive a formula which shows the explicit connection between local conservation\nand approximate decoherence. We then consider a class of models consisting of a\nlarge number of weakly interacting components, in which the projections onto\nlocal densities may be decomposed into projections onto one of two alternatives\nof the individual components. The main example we consider is a one-dimensional\nchain of locally coupled spins, and the projections are onto the total spin in\na subsection of the chain. We compute the decoherence functional for histories\nof local densities, in the limit when the number of components is very large.\nWe find that decoherence requires two things: the smearing volumes must be\nsufficiently large to ensure approximate conservation, and the local densities\nmust be partitioned into sufficiently large ranges to ensure protection against\nquantum fluctuations.",
"arxiv_id": "quant-ph/9601004",
"authors": [
"T. A. Brun",
"J. J. Halliwell"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"doi": "10.1103/PhysRevD.54.2899",
"journal_ref": "Phys.Rev.D54:2899-2912,1996",
"title": "Decoherence of Hydrodynamic Histories: A Simple Spin Model",
"url": "https://arxiv.org/abs/quant-ph/9601004"
},
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