Semiclassical properties and chaos degree for the quantum Baker's map

Journal of Mathematical Physics

Volumn 43, Issue 2, 2002, Pages 734-755

  Inoue, Kei ^a   Ohya, Masanori ^a   Volovich, Igor V ^b  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981882     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1420743     Document Type: Article

References (38)

1. Dynamical Systems, edited by D.V. Anosov and V.I. Arnold (VINITI, Moscow, 1996).
2. Ya. G. Sinai, Introduction to Ergodic Theory (Fasis, Moscow, 1996).
3. M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990).
4. Quantum Chaos: Between Order and Disorder, edited by G. Casati and B.V. Chirikov (Cambridge University Press, Cambridge, 1995).
5. I.Y. Arefeva, P.B. Medvedev, O.A. Rytchkov, and I.V. Volovich, Chaos, Solitons Fractals 10(2-3), 213 (1999).
6. K. Hepp, Commun. Math. Phys. 35, 265 (1974).
7. W.H. Zurek, Phys. Rev. D 24, 1516 (1981).
8. W.H. Zurek, quant-ph/015127.
9. G.G. Emch, H. Narnhofer, W. Thirring, and G.L. Sewell, J. Math. Phys. 35, 5582 (1994).
10. H. Hasegawa, Open Syst. Inf. Dyn. 4, 359 (1997).
11. V.P. Maslov, Perturbation Theory and Asymptotic Methods (MGU, Moscow, 1965).
12. G.P. Berman and G.M. Zaslavsky, Physica A 91A, 450 (1976).
13. G.M. Zaslavskii, Stochasticity of Dynamical Systems (Nauka, Moscow, 1984).
14. M.V. Berry, Some Quantum to Classical Asymptotics, Les Houches Summer School "Chaos and quantum physics," edited by M.J. Giannoni, A. Voros, and Z. Justi (North-Holland, Amsterdam, 1991).
15. N.L. Balazs and A. Voros, Ann. Phys. 190, 1 (1989).
16. A.M. Ozorio de Almeida and M. Saraceno, Ann. Phys. 210, 1 (1991).
17. F.M. Dittes, E. Doron, and U. Smilansky, Phys. Rev. E 49, R963 (1994).
18. M. Saraceno and A. Voros, Physica D 79, 206 (1994).
19. L. Kaplan and E.J. Heller, Phys. Rev. Lett. 76, 1453 (1996).
20. M.G.E. da Luz and A.M. Ozorio de Almeida, Nonlinearity 8, 43 (1995).
21. R. Schack and C.M. Caves, Phys. Rev. Lett. 71, 525 (1993).
22. R. Schack and C.M. Caves, Phys. Rev. E 53, 3257 (1996).
23. P.W. O'Connor and S. Tomsovic, Ann. Phys. 207, 218 (1991).
24. M. Ohya, Int. J. Theor. Phys. 37(1), 495 (1998).
25. R.S. Ingarden, A. Kossakowski, and M. Ohya, Information Dynamics and Open Systems (Kluwer Academic, Dordrecht, 1997).
26. K. Inoue, M. Ohya, and K. Sato, Chaos, Solitons Fractals 11, 1377 (2000).
27. M. Saraceno, Ann. Phys. 199, 37 (1990).
28. J.H. Hannay, J.P. Keating, and A.M. Ozorio de Almeida, Nonlinearity 7, 1327 (1994).
29. R. Schack, Phys. Rev. A 57, 1634 (1998).
30. T. Brun and R. Schack, Phys. Rev. A 59, 2649 (1999).
31. A. Lakshminarayan and N.L. Balazs, Ann. Phys. 226, 350 (1993).
32. A. Lakshminarayan, Ann. Phys. 239, 272 (1995).
33. R. Schack and C.M. Caves, Applic. Alg. Eng. Commun. Comput. AAECC 10, 305 (2000).
34. V.M. Alekseev and M.N. Yakobson, Phys. Rep. 75, 287 (1981).
35. A.N. Soklakov and R. Schack, quant-ph/9908040.
36. A.N. Soklakov and R. Schack, quant-ph/0107071.
37. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
38. K. Inoue, M. Ohya, and I.V. Volovich, quant-ph/0108107.