Cover image for A Measure Theoretical Approach to Quantum Stochastic Processes
Başlık:
A Measure Theoretical Approach to Quantum Stochastic Processes
Yazar:
Waldenfels, Wilhelm von. author.
ISBN:
9783642450822
Fiziksel Tanım:
XVII, 228 p. online resource.
Series:
Lecture Notes in Physics, 878
Contents:
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.
Abstract:
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.
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