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Measure theoretical approach to quantum stochastic processes / Wilhelm Von Waldenfels.

By: Material type: TextTextSeries: Lecture notes in physics ; v 878.Publication details: Berlin : Springer-Verlag, 2014.Description: xvii, 228 p ; 24 cmISBN:
  • 9783642450815 (soft cover : alk. paper)
Subject(s): DDC classification:
  • 530.120151542 23 V948
Contents:
1. Weyl Algebras -- 2. Continuous Sets of Creation and Annihilation Operators -- 3. One-Parameter Groups -- 4. Four Explicitly Calculable One-Excitation Processes -- 5. White Noise Calculus -- 6. Circled Integrals -- 7. White Noise Integration -- 8. The Hudson-Parthasarathy Differential Equation -- 9. The Amplifies Oscillator -- 10. Approximation by Coloured Noise -- References -- Index.
Summary: 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 530.120151542 V948 (Browse shelf(Opens below)) Available 136660
Total holds: 0

Includes bibliographical references and index.

1. Weyl Algebras --
2. Continuous Sets of Creation and Annihilation Operators --
3. One-Parameter Groups --
4. Four Explicitly Calculable One-Excitation Processes --
5. White Noise Calculus --
6. Circled Integrals --
7. White Noise Integration --
8. The Hudson-Parthasarathy Differential Equation --
9. The Amplifies Oscillator --
10. Approximation by Coloured Noise --
References --
Index.

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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