Quantum-classical correspondences of the Berry-Robnik parameter through bifurcations in lemon billiard systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 5, 2001, Pages

  Makino, H ^a   Harayama, T ^b   Aizawa, Y ^a  

^a WASEDA UNIVERSITY   (Japan)

^b ADVANCED TELECOMMUNICATIONS RESEARCH INSTITUTE INTERNATIONAL   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; HAMILTONIANS; MAPPING; MATHEMATICAL MODELS; MATRIX ALGEBRA; POISSON DISTRIBUTION; TIME VARYING SYSTEMS;

BERRY-ROBNIK FORMULAE; LEMON BILLIARDS MODEL;

QUANTUM THEORY;

EID: 0035335467     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.056203     Document Type: Article

References (26)

1. M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356, 375 (1977).
2. G. Casati, B. V. Chirikov, and I. Guarneri, Phys. Rev. Lett. 54, 1350 (1985).
3. O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
4. F. Borgonovi, G. Casati, and B. Li, Phys. Rev. Lett. 77, 4744 (1996).
5. M. Robnik, J. Phys. A 17, 1049 (1984).
6. T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984).
7. T. Terasaka and T. Matsushita, Phys. Rev. A 32, 538 (1985).
8. H. D. Meyer, E. Haller, H. Köppel, and L. S. Cederbaum, J. Phys. A 17, L831 (1984).
9. V. Lopac, I. Mrkonjić, and D. Radić, Phys. Rev. E 59, 303 (1999).
10. M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984).
11. M. Robnik, Nonlin. Phenom. Complex Syst. 1, 1 (1998).
12. M. Robnik and T. Prosen, J. Phys. A 30, 8787 (1997).
13. T. Prosen and M. Robnik, J. Phys. A 26, 2371 (1993).
14. T. Prosen and M. Robnik, J. Phys. A 27, 8059 (1994).
15. T. Prosen, Physica D 91, 244 (1996).
16. T. Prosen, J. Phys. A 31, 7023 (1998).
17. H. Makino, T. Harayama, and Y. Aizawa, Prog. Theor. Phys. Suppl. 139, 477 (2000).
18. B. Li and M. Robnik, J. Phys. A 28, 4843 (1995).
19. H. Makino, T. Harayama, and Y. Aizawa, Phys. Rev. E 59, 4026 (1999).
20. E. J. Heller and S. Tomsovic, Phys. Today 46(7), 38 (1993).
21. S. Ree and L. E. Reichl, Phys. Rev. E 60, 1607 (1999).
22. G. D. Birkhoff, Dynamical Systems (American Mathematical Society, Providence, RI, 1927; reprinted 1996).
23. T. Harayama, A. Shudo, and T. Tasaki, Nonlinearity 12, 1113 (1999).
24. R. S. MacKay and J. D. Meiss, Phys. Lett. 92A, 98 (1983).
25. H. D. Meyer, J. Chem. Phys. 84, 3147 (1985).
26. P. Jacquod and J. P. Amiet, J. Chem. Phys. 28, 4799 (1995).