dorsal/arxiv
View SchemaInvitation to quantum dynamical semigroups
| Authors | Robert Alicki |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205188 |
| URL | https://arxiv.org/abs/quant-ph/0205188 |
Abstract
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general mathematical structures is discussed. Then basic derivation schemes of the constructive approach including singular coupling, weak coupling and low density limits are presented in their higly simplified versions. Two-level system coupled to a heat bath, damped harmonic oscillator, models of decoherence, quantum Brownian particle and Bloch-Boltzmann equations are used as illustrations of the general theory. Physical and mathematical limitations of the quantum open system theory, the validity of Markovian approximation and alternative approaches are discussed also.
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"abstract": "The theory of quantum dynamical semigroups within the mathematically rigorous\nframework of completely positive dynamical maps is reviewed. First, the\naxiomatic approach which deals with phenomenological constructions and general\nmathematical structures is discussed. Then basic derivation schemes of the\nconstructive approach including singular coupling, weak coupling and low\ndensity limits are presented in their higly simplified versions. Two-level\nsystem coupled to a heat bath, damped harmonic oscillator, models of\ndecoherence, quantum Brownian particle and Bloch-Boltzmann equations are used\nas illustrations of the general theory. Physical and mathematical limitations\nof the quantum open system theory, the validity of Markovian approximation and\nalternative approaches are discussed also.",
"arxiv_id": "quant-ph/0205188",
"authors": [
"Robert Alicki"
],
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"quant-ph"
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"title": "Invitation to quantum dynamical semigroups",
"url": "https://arxiv.org/abs/quant-ph/0205188"
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