A measure theoretical approach to quantum stochastic processes Wilhelm von Waldenfels

Format:

Book

Author/Creator:

Waldenfels, W. von (Wilhelm), 1932- author.

Series:

Lecture notes in physics ; 0075-8450 878

Lecture notes in physics 0075-8450 volume 878

Language:

English

Subjects (All):

Quantum measure theory.

Quantum statistics.

Stochastic processes--Mathematical models.

Stochastic processes.

Physical Description:

1 online resource

Place of Publication:

Heidelberg Springer 2014

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

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

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed March 20, 2014)

Other Format:

Printed edition:

ISBN:

9783642450822

3642450822

OCLC:

869939293

Access Restriction:

Restricted for use by site license