A Measure Theoretical Approach to Quantum Stochastic Processes

A Measure Theoretical Approach to Quantum Stochastic Processes

by Wilhelm Waldenfels


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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.

Product Details

ISBN-13: 9783642450815
Publisher: Springer Berlin Heidelberg
Publication date: 11/29/2013
Series: Lecture Notes in Physics , #878
Edition description: 2014
Pages: 228
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of 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.

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