dorsal/arxiv
View SchemaTime as a statistical variable and intrinsic decoherence
| Authors | Rodolfo Bonifacio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9902029 |
| URL | https://arxiv.org/abs/quant-ph/9902029 |
| DOI | 10.1063/1.57868 |
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 specific 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 as if time evolution would take place randomly at average intervals t2, each evolution having a time width t1. A generalized Tam Mandelstam inequality is derived. The relation with previous work by Milburn is discussed. The agreement with recent experiments on damped Rabi oscillations is 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 specific\nstatistical assumptions we find a generalized Liouville equation which depends\non two characteristic time t1 and t2 and reduces to the usual equation in the\nlimit t1 = t2 --\u003e 0. However, for t1 and t2 arbitrarily small but finite, our\nequation can be written as a finite difference equation which predicts state\nreduction to the diagonal form in the energy representation. The rate of\ndecoherence becomes faster at the macroscopic limit as the energy scale of the\nsystem increases. In our approach the evolution time appears, a posteriori, as\na statistical variable as if time evolution would take place randomly at\naverage intervals t2, each evolution having a time width t1. A generalized Tam\nMandelstam inequality is derived. The relation with previous work by Milburn is\ndiscussed. The agreement with recent experiments on damped Rabi oscillations is\ndescribed.",
"arxiv_id": "quant-ph/9902029",
"authors": [
"Rodolfo Bonifacio"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.57868",
"title": "Time as a statistical variable and intrinsic decoherence",
"url": "https://arxiv.org/abs/quant-ph/9902029"
},
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