A measure theoretical approach to quantum stochastic processes
This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, w...
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| Main Author: | |
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| Format: | Book/Monograph |
| Language: | English |
| Published: |
Heidelberg New York Dordrecht London
Springer
2014
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| Series: | Lecture notes in physics
878 |
| In: |
Lecture notes in physics (878)
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| DOI: | 10.1007/978-3-642-45082-2 |
| Subjects: | |
| Online Access: | Verlag, Volltext: https://doi.org/10.1007/978-3-642-45082-2 Resolving-System, lizenzpflichtig, Volltext: http://dx.doi.org/10.1007/978-3-642-45082-2 Cover: https://swbplus.bsz-bw.de/bsz398204888cov.jpg Verlag, Zentralblatt MATH, Inhaltstext: https://zbmath.org/?q=an:1291.81005 
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| Author Notes: | by Wilhelm Waldenfels |
| Summary: | This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included |
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| Physical Description: | Online Resource |
| ISBN: | 9783642450822 |
| DOI: | 10.1007/978-3-642-45082-2 |