dorsal/arxiv
View SchemaTime as a statistical variable and intrinsic decoherence
| Authors | Rodolfo Bonifacio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9901063 |
| URL | https://arxiv.org/abs/quant-ph/9901063 |
| Journal | Nuovo Cim. B114 (1999) 473-488 |
Abstract
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard quantum mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the unitarity requirement. With no approximations and statistical assumptions we find a generalized Liouville equation which depends on two characteristic time t1 and t2 and reduces to the usual equation in the limit t1 = t2 -> 0. However, for t1 and t2 arbitrarily small but finite, our equation can be written as a finite difference equation which predicts state reduction to the diagonal form in the energy representation. The rate of decoherence becomes faster at the macroscopic limit as the energy scale of the system increases. In our approach the evolution time appears, a posteriori, as a statistical variable with a Poisson-gamma function probability distribution as if time evolution would take place randomly at average intervals t2 each evolution having a time width t1. This view point is supported by the derivation of a generalized Tam Mandelstam inequality. The relation with previous work by Milburn, with laser and micromaser theory and many experimental testable examples are described.
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"abstract": "We propose a novel approach to intrinsic decoherence without adding new\nassumptions to standard quantum mechanics. We generalize the Liouville equation\njust by requiring the dynamical semigroup property of time evolution and\ndropping the unitarity requirement. With no approximations and statistical\nassumptions we find a generalized Liouville equation which depends on two\ncharacteristic time t1 and t2 and reduces to the usual equation in the limit t1\n= t2 -\u003e 0. However, for t1 and t2 arbitrarily small but finite, our equation\ncan be written as a finite difference equation which predicts state reduction\nto the diagonal form in the energy representation. The rate of decoherence\nbecomes faster at the macroscopic limit as the energy scale of the system\nincreases. In our approach the evolution time appears, a posteriori, as a\nstatistical variable with a Poisson-gamma function probability distribution as\nif time evolution would take place randomly at average intervals t2 each\nevolution having a time width t1. This view point is supported by the\nderivation of a generalized Tam Mandelstam inequality. The relation with\nprevious work by Milburn, with laser and micromaser theory and many\nexperimental testable examples are described.",
"arxiv_id": "quant-ph/9901063",
"authors": [
"Rodolfo Bonifacio"
],
"categories": [
"quant-ph"
],
"journal_ref": "Nuovo Cim. B114 (1999) 473-488",
"title": "Time as a statistical variable and intrinsic decoherence",
"url": "https://arxiv.org/abs/quant-ph/9901063"
},
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