A Measure Theoretical Approach to Quantum Stochastic Processes

✍ Scribed by Wilhelm von Waldenfels (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2014
• Tongue: English
• Leaves: 241
• Series: Lecture Notes in Physics 878
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XVII
Weyl Algebras....Pages 1-23
Continuous Sets of Creation and Annihilation Operators....Pages 25-38
One-Parameter Groups....Pages 39-54
Four Explicitly Calculable One-Excitation Processes....Pages 55-95
White Noise Calculus....Pages 97-112
Circled Integrals....Pages 113-121
White Noise Integration....Pages 123-138
The Hudson-Parthasarathy Differential Equation....Pages 139-177
The Amplified Oscillator....Pages 179-212
Approximation by Coloured Noise....Pages 213-223
Back Matter....Pages 225-228

✦ Subjects

Quantum Physics; Mathematical Physics; Mathematical Methods in Physics