Lecture Notes in Physics

A Measure Theoretical Approach to Quantum Stochastic Processes

Authors: von Waldenfels, Wilhelm

  • Authored by a leading researcher in the field
  • Self-contained presentation of the subject matter
  • Examines a number of worked examples in detail
see more benefits

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-45082-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-642-45081-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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.

Reviews

From the book reviews:

“This monograph represents a nice survey written in a concise and lucid manner, enabling the reader to quickly and easily grasp the main aspects and ideas of quantum stochastic processes. … The book is suitable for graduate students or researchers who work in the field of mathematics and physics.” (Dora Seleši, Mathematical Reviews, February, 2015)


Table of contents (10 chapters)

  • Weyl Algebras

    Waldenfels, Wilhelm

    Pages 1-23

  • Continuous Sets of Creation and Annihilation Operators

    Waldenfels, Wilhelm

    Pages 25-38

  • One-Parameter Groups

    Waldenfels, Wilhelm

    Pages 39-54

  • Four Explicitly Calculable One-Excitation Processes

    Waldenfels, Wilhelm

    Pages 55-95

  • White Noise Calculus

    Waldenfels, Wilhelm

    Pages 97-112

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-45082-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-642-45081-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
A Measure Theoretical Approach to Quantum Stochastic Processes
Authors
Series Title
Lecture Notes in Physics
Series Volume
878
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-45082-2
DOI
10.1007/978-3-642-45082-2
Softcover ISBN
978-3-642-45081-5
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XVII, 228
Topics