TY  - BOOK
AU  - Von Waldenfels,Wilhelm
TI  - Measure theoretical approach to quantum stochastic processes
T2  - Lecture notes in physics
SN  - 9783642450815 (soft cover : alk. paper)
U1  - 530.120151542 23
PY  - 2014///
CY  - Berlin
PB  - Springer-Verlag
KW  - Quantum measure theory
KW  - Quantum statistics.
KW  - Stochastic processes
KW  - Mathematical models.
N1  - Includes bibliographical references and index; 1. Weyl Algebras --
2. Continuous Sets of Creation and Annihilation Operators --
3. One-Parameter Groups --
4. Four Explicitly Calculable One-Excitation Processes --
5. White Noise Calculus --
6. Circled Integrals --
7. White Noise Integration --
8. The Hudson-Parthasarathy Differential Equation --
9. The Amplifies Oscillator --
10. Approximation by Coloured Noise --
References --
Index
N2  - 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.
ER  -