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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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2014, 2014
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| Edition: | 1st ed. 2014 |
| Series: | Lecture Notes in Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
| 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: | XVII, 228 p online resource |
| ISBN: | 9783642450822 |