dorsal/arxiv
View SchemaDecoherent Histories and Hydrodynamic Equations
| Authors | J. J. Halliwell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9805062 |
| URL | https://arxiv.org/abs/quant-ph/9805062 |
| DOI | 10.1103/PhysRevD.58.105015 |
| Journal | Phys.Rev. D58 (1998) 105015 |
Abstract
For a system consisting of a large collection of particles, a set of variables that will generally become effectively classical are the local densities (number, momentum, energy). That is, in the context of the decoherent histories approach to quantum theory, it is expected that histories of these variables will be approximately decoherent, and that their probabilites will be strongly peaked about hydrodynamic equations. This possibility is explored for the case of the diffusion of the number density of a dilute concentration of foreign particles in a fluid. This system has the appealing feature that the microscopic dynamics of each individual foreign particle is readily obtained and the approach to local equilibrium may be seen explicitly. It is shown that, for certain physically reasonable initial states, the probabilities for histories of number density are strongly peaked about evolution according to the diffusion equation. Decoherence of these histories is also shown for a class of initial states which includes non-trivial superpositions of number density. Histories of phase space densities are also discussed. The case of histories of number, momentum and energy density for more general systems, such as a dilute gas, is also discussed in outline. When the initial state is a local equilibrium state, it is shown that the histories are trivally decoherent, and that the probabilities for histories are peaked about hydrodynamic equations. An argument for decoherence of more general initial states is given.
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"abstract": "For a system consisting of a large collection of particles, a set of\nvariables that will generally become effectively classical are the local\ndensities (number, momentum, energy). That is, in the context of the decoherent\nhistories approach to quantum theory, it is expected that histories of these\nvariables will be approximately decoherent, and that their probabilites will be\nstrongly peaked about hydrodynamic equations. This possibility is explored for\nthe case of the diffusion of the number density of a dilute concentration of\nforeign particles in a fluid. This system has the appealing feature that the\nmicroscopic dynamics of each individual foreign particle is readily obtained\nand the approach to local equilibrium may be seen explicitly. It is shown that,\nfor certain physically reasonable initial states, the probabilities for\nhistories of number density are strongly peaked about evolution according to\nthe diffusion equation. Decoherence of these histories is also shown for a\nclass of initial states which includes non-trivial superpositions of number\ndensity. Histories of phase space densities are also discussed. The case of\nhistories of number, momentum and energy density for more general systems, such\nas a dilute gas, is also discussed in outline. When the initial state is a\nlocal equilibrium state, it is shown that the histories are trivally\ndecoherent, and that the probabilities for histories are peaked about\nhydrodynamic equations. An argument for decoherence of more general initial\nstates is given.",
"arxiv_id": "quant-ph/9805062",
"authors": [
"J. J. Halliwell"
],
"categories": [
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"doi": "10.1103/PhysRevD.58.105015",
"journal_ref": "Phys.Rev. D58 (1998) 105015",
"title": "Decoherent Histories and Hydrodynamic Equations",
"url": "https://arxiv.org/abs/quant-ph/9805062"
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