Quantum Stochastic Processes and Noncommutative Geometry
eBook - PDF

Quantum Stochastic Processes and Noncommutative Geometry

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Quantum Stochastic Processes and Noncommutative Geometry

About this book

The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.

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Yes, you can access Quantum Stochastic Processes and Noncommutative Geometry by Kalyan B. Sinha,Debashish Goswami in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. Notation
  8. 1 Introduction
  9. 2 Preliminaries
  10. 3 Quantum dynamical semigroups
  11. 4 Hilbert modules
  12. 5 Quantum stochastic calculus with bounded coefficients
  13. 6 Dilation of quantum dynamical semigroups with bounded generator
  14. 7 Quantum stochastic calculus with unbounded coefficients
  15. 8 Dilation of quantum dynamical semigroups with unbounded generator
  16. 9 Noncommutative geometry and quantum stochastic processes
  17. References
  18. Index