A measure theoretical approach to quantum stochastic processes /
Waldenfels, W. von 1932-
A measure theoretical approach to quantum stochastic processes / Wilhelm von Waldenfels. - 1 online resource (xvii, 228 pages) - Lecture notes in physics, volume 878 0075-8450 ; . - Lecture notes in physics ; 878. .
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.
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.
9783642450822 3642450822
10.1007/978-3-642-45082-2 doi
Quantum measure theory.
Quantum statistics.
Stochastic processes--Mathematical models.
Théorie quantique de la mesure.
Statistique quantique.
Processus stochastiques--Modèles mathématiques.
Physique.
Astronomie.
Quantum measure theory
Quantum statistics
Stochastic processes--Mathematical models
QC174.17.M4
530.1201/51542
A measure theoretical approach to quantum stochastic processes / Wilhelm von Waldenfels. - 1 online resource (xvii, 228 pages) - Lecture notes in physics, volume 878 0075-8450 ; . - Lecture notes in physics ; 878. .
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.
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.
9783642450822 3642450822
10.1007/978-3-642-45082-2 doi
Quantum measure theory.
Quantum statistics.
Stochastic processes--Mathematical models.
Théorie quantique de la mesure.
Statistique quantique.
Processus stochastiques--Modèles mathématiques.
Physique.
Astronomie.
Quantum measure theory
Quantum statistics
Stochastic processes--Mathematical models
QC174.17.M4
530.1201/51542