A Measure Theoretical Approach to Quantum Stochastic Processes
Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
| Author: | Wilhelm Waldenfels | ISBN: | 9783642450822 |
| Publisher: | Springer Berlin Heidelberg | Publication: | November 29, 2013 |
| Imprint: | Springer | Language: | English |
| Author: | Wilhelm Waldenfels |
| ISBN: | 9783642450822 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | November 29, 2013 |
| Imprint: | Springer |
| Language: | English |
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.
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.
