TY  - BOOK
AU  - Waldenfels,W.von
TI  - A measure theoretical approach to quantum stochastic processes
T2  - Lecture notes in physics,
SN  - 9783642450822
AV  - QC174.17.M4 
U1  - 530.1201/51542 23
PY  - 2014///
CY  - Heidelberg
PB  - Springer
KW  - Quantum measure theory
KW  - Quantum statistics
KW  - Stochastic processes
KW  - Mathematical models
KW  - Théorie quantique de la mesure
KW  - Statistique quantique
KW  - Processus stochastiques
KW  - Modèles mathématiques
KW  - Physique
KW  - eclas
KW  - Astronomie
KW  - fast
N1  - Includes bibliographical references and index; Weyl Algebras -- Continuous Sets of Creation and Annihilation Operators -- One-Parameter Groups -- Four Explicitly Calculable One-Excitation Processes -- White Noise Calculus -- Circled Integrals -- White Noise Integration -- The Hudson-Parthasarathy Differential Equation -- The Amplifies Oscillator -- Approximation by Coloured Noise
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
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-642-45082-2
ER  -