A Measure Theoretical Approach to Quantum Stochastic Processes

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Beschreibung

Starting from the premise that abstract quantum stochastic processes can be understood as a quantum field theory in one space and time coordinate, this guide considers a number of representative examples and covers advanced topics such as white noise calculus.


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.



Authored by a leading researcher in the field

Self-contained presentation of the subject matter

Examines a number of worked examples in detail



Inhalt

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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Produktinformationen

Titel
A Measure Theoretical Approach to Quantum Stochastic Processes
Autor
EAN
9783642450815
ISBN
3642450814
Format
Kartonierter Einband
Herausgeber
Springer Berlin Heidelberg
Anzahl Seiten
248
Gewicht
382g
Größe
H235mm x B155mm x T13mm
Jahr
2013
Untertitel
Englisch
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