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A Measure Theoretical Approach to Quantum Stochastic Processes

A Measure Theoretical Approach to Quantum Stochastic Processes Image

Book Details:

Publisher:Springer
Series: Springer
Author:W. von Waldenfels
Edition:1
ISBN-10:3642450814
ISBN-13:9783642450815
Pages:228
Published:Dec 31 2013
Posted:Dec 13 2014
Language:English
Book format:PDF
Book size:1.52 MB

Book Description:

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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