A Measure Theoretical Approach to Quantum Stochastic Processes
Waldenfels, Wilhelm von.
A Measure Theoretical Approach to Quantum Stochastic Processes [electronic resource] / by Wilhelm von Waldenfels. - XVII, 228 p. online resource. - Lecture Notes in Physics, 878 0075-8450 ; . - Lecture Notes in Physics, 878 .
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 -- Index.
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
10.1007/978-3-642-45082-2 doi
Quantum theory.
Mathematical physics.
Quantum Physics.
Mathematical Physics.
Mathematical Methods in Physics.
QC173.96-174.52
530.12
A Measure Theoretical Approach to Quantum Stochastic Processes [electronic resource] / by Wilhelm von Waldenfels. - XVII, 228 p. online resource. - Lecture Notes in Physics, 878 0075-8450 ; . - Lecture Notes in Physics, 878 .
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 -- Index.
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
10.1007/978-3-642-45082-2 doi
Quantum theory.
Mathematical physics.
Quantum Physics.
Mathematical Physics.
Mathematical Methods in Physics.
QC173.96-174.52
530.12