A Measure Theoretical Approach to Quantum Stochastic Processes
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A Measure Theoretical Approach to Quantum Stochastic Processes

SKU: 9783642450822

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Additional information

Full Title

A Measure Theoretical Approach to Quantum Stochastic Processes
Author(s)

Wilhelm Waldenfels
Edition
ISBN

9783642450822, 9783642450815
Publisher

Springer
Format

PDF and EPUB

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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