Advertisement

Quantum Signatures of Chaos

  • Fritz Haake
  • Sven Gnutzmann
  • Marek Kuś

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 1-14
  3. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 15-70
  4. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 71-84
  5. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 85-109
  6. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 111-203
  7. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 205-288
  8. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 289-302
  9. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 303-363
  10. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 365-407
  11. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 409-510
  12. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 511-589
  13. Fritz Haake, Sven Gnutzmann, Marek Kuś
    Pages 591-653
  14. Back Matter
    Pages 655-659

About this book

Introduction

This by now classic text provides an excellent introduction to and survey of the still-expanding field of quantum chaos. For this long-awaited fourth edition, the original text has been thoroughly modernized.

The topics include a brief introduction to classical Hamiltonian chaos, a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria used to distinguish regular and irregular motion, and antiunitary (generalized time reversal) and unitary symmetries. The standard Wigner-Dyson symmetry classes, as well as the non-standard ones introduced by Altland and Zirnbauer, are investigated and illustrated with numerous examples. Random matrix theory is presented in terms of both classic methods and the supersymmetric sigma model. The power of the latter method is revealed by applications outside random-matrix theory, such as to quantum localization, quantum graphs, and universal spectral fluctuations of individual chaotic dynamics. The equivalence of the sigma model and Gutzwiller’s semiclassical periodic-orbit theory is demonstrated. Last but not least, the quantum mechanics of dissipative chaotic systems are also briefly described. 

Each chapter is accompanied by a selection of problems that will help newcomers test and deepen their understanding, and gain a firm command of the methods presented.

Keywords

classical Hamiltonian chaos dissipative systems level dynamics quantum localization quantum time evolution universal spectral fluctuations Random matrix theory

Authors and affiliations

  • Fritz Haake
    • 1
  • Sven Gnutzmann
    • 2
  • Marek Kuś
    • 3
  1. 1.Universität Duisburg-EssenEssenGermany
  2. 2.School of Mathematical Science, University of NottinghamNottinghamUK
  3. 3.Center for Theoretical Physics, Polish Academy of SciencesWarszawaPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-97580-1
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-97579-5
  • Online ISBN 978-3-319-97580-1
  • Series Print ISSN 0172-7389
  • Series Online ISSN 2198-333X
  • Buy this book on publisher's site