A Measure Theoretical Approach to Quantum Stochastic Processes

  • Wilhelm von Waldenfels

Part of the Lecture Notes in Physics book series (LNP, volume 878)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Wilhelm von Waldenfels
    Pages 1-23
  3. Wilhelm von Waldenfels
    Pages 25-38
  4. Wilhelm von Waldenfels
    Pages 39-54
  5. Wilhelm von Waldenfels
    Pages 55-95
  6. Wilhelm von Waldenfels
    Pages 97-112
  7. Wilhelm von Waldenfels
    Pages 113-121
  8. Wilhelm von Waldenfels
    Pages 123-138
  9. Wilhelm von Waldenfels
    Pages 139-177
  10. Wilhelm von Waldenfels
    Pages 179-212
  11. Wilhelm von Waldenfels
    Pages 213-223
  12. Back Matter
    Pages 225-228

About this book


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.


Classical measure theory Hudson-Parthasarathy equation Quantum stochastic processes Spectral decomposition of Hamilton operator White noise calculus

Authors and affiliations

  • Wilhelm von Waldenfels
    • 1
  1. 1.HimmelpfortGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-45082-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-45081-5
  • Online ISBN 978-3-642-45082-2
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • About this book