How can we observe and describe chaos?

Open Systems and Information Dynamics

Volumn 10, Issue 3, 2003, Pages 221-233

  Kossakowski, Andrzej ^a   Ohya, Masanori ^b   Togawa, Yoshio ^b  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

^b TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4043133089     PISSN: 12301612     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025123923519     Document Type: Article

References (24)

1. L. Accardi, M. Ohya, and N. Watanabe, Dynamical entropy through quantum Markov chain, Open Sys. Information Dyn. 4, 71 (1997).
2. K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos - An Introduction to Dynamical Systems, Textbooks in Mathematical Sciences, Springer, 1996.
3. R. Alicki and M. Fannes, Defining quantum dynamical entropy, Lett. Math. Physics 32, 75 (1994).
4. F. Benatti, Deterministic Chaos in Infinite Quantum Systems, Springer, 1993.
5. R. L. Devaney, An Introduction to Chaotic dynamical Systems, Benjamin, 1986.
6. G. Casati and B. Chirikov, Quantum Chaos: Between Order and Disorder, Cambridge University Press, 1995.
7. G. G. Emch, H. Narnhofer, W. Thirring, and G. L. Sewell, Anosov actions on noncommutative algebras, J. Math. Phys. 35, No. 11, 5582 (1994).
8. H. Hasegawa, Dynamical formulation of quantum level statistics, Open Sys. Information Dyn. 4, 359 (1997).
9. R. S. Ingarden, A. Kossakowski, and M. Ohya, Information Dynamics and Open Systems, Kluwer Academic Publishers, 1997.
10. K. Inoue, M. Ohya, and A. Kossakowski, A Description of Quantum Chaos, preprint, 2002.
11. K. Inoue, M. Ohya, and K. Sato, Application of chaos degree to some dynamical systems, Chaos, Solitons & Fractals 11, 1377-1385 (2000).
12. K. Inoue, M. Ohya, and V. Volovich, Semiclassical properties and chaos degree for the quantum baker's map, Journal of Mathematical Physics 43, 734 (2002).
13. K. Inoue, M. Ohya, and I. V. Volovich, On quantum-classical correspondence for baker's map, quant-ph/0108107.
14. A. Kossakowski, M. Ohya, and N. Watanabe, Quantum dynamical entropy for completely positive maps, Infinite Dimensional Analysis, Quantum Probability and Related Topics 2, 267 (1999).
15. W. A. Majewski, Does quantum chaos exitst? A quantum Lyapunov exponents approach, quant-ph/9805068.
16. N. Muraki and M. Ohya, Entropy functionals of Kolmogorov Sinai type and their limit theorems, Lett. Math. Phys. 36, 327 (1996).
17. M. Ohya, Some aspects of quantum information theory and their applications to irreversible processes, Rep. Math. Phys. 27, 19 (1989).
18. M. Ohya, Information dynamics and its applications to optical communication processes, Lecture Note in Physics 378, 81 (1991).
19. M. Ohya, State change, complexity and fractal in quantum systems, Quantum Communications and Measurement, Plenum Press, New York, 1995, pp. 309-320.
20. M. Ohya, Complexity and fractal dimensions for quantum states, Open Sys. Information Dyn. 4, 141 (1997).
21. M. Ohya, Complexities and their applications to characterization of chaos, International Journal of Theoretical Physics 37, 495 (1998).
22. M. Ohya, Complexity in Quantum System and its Application to Brain Function in: Quantum Information II, T. Hida and K. Saito, ed., World Scientific, 2000.
23. M. Ohya and D. Petz, Quantum Entropy and Its Use, Springer-Verlag, TMP, (1993).
24. A. Kossakowski, M. Ohya and Y. Togawa, in preparation.