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© 2015

Quantum Quadratic Operators and Processes

Benefits

  • Provides a self-contained treatment of nonlinear Markov evolution, with a focus on (classical and quantum) quadratic operators and the asymptotic behavior of the dynamical systems they generate

  • This is the first book to study both classical and quantum (non-commutative) nonlinear dynamics using the theory of Markov processes

  • Covers the most recent developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes

  • Includes material which has potential applications to quantum information theory

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2133)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 1-5
  3. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 7-30
  4. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 31-59
  5. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 61-84
  6. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 85-101
  7. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 103-146
  8. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 147-171
  9. Farrukh Mukhamedov, Nasir Ganikhodjaev
    Pages 173-216
  10. Back Matter
    Pages 217-234

About this book

Introduction

Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels.

This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting  problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.

Keywords

37A50;47D07;37A30;37A55;46L53;81P16; dynamics of quadratic stochastic operator marginal Markov processes quantum quadratic operator quantum quadratic stochastic procesess regularity, ergodicity and mixing properties

Authors and affiliations

  1. 1.Dept. of Comput. & Theor. SciencesInternational Islamic University MalaysiaKuantanMalaysia
  2. 2.Dept. of Comput. & Theor. SciencesInternational Islamic University MalaysiaKuantanMalaysia

Bibliographic information

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