Scars in nonintegrable and rational billiards

Journal of Statistical Physics

Volumn 83, Issue 1-2, 1996, Pages 215-242

  Tomiya, M ^a   Yoshinaga, N ^b  

^a SEIKEI UNIVERSITY   (Japan)

^b SAITAMA UNIVERSITY   (Japan)

Author keywords

Bunimovich stadium; Pseudointegrable systems; Quantum chaos; Rational billiard

Indexed keywords

EID: 0030556272     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02183647     Document Type: Article

References (19)

1. M. V. Berry, In Semiclassical Mechanics Regular and Irregular Motion (Les Houches, Session XXXVI, 1981), G. Iooss, R. H. G. Helleman, and R. Stora, eds. (North-Holland, Amsterdam, 1983), p. 171.
2. A. N. Zemlyalov and A. B. Katoh, Math Notes 18:760 (1976); 20:1051 (1976).
3. A. N. Zemlyalov and A. B. Katoh, Math Notes 18:760 (1976); 20:1051 (1976).
4. P. J. Richens and M. V. Berry, Physica D 2:495 (1981).
5. B. Eckhardt, J. Ford, and F. Vivaldi, Physica D 13:329 (1984).
6. J. L. Vega, T. Uzer and J. Ford, Phys. Rev. E 48:3414 (1993).
7. T. Cheon and T. D. Cohen, Phys. Rev. Lett. 62:1769 (1989).
8. A. Shudo and Y. Shimizu, Phys. Rev. E 47:54 (1993).
9. E. Heller, in Wavepacket Dynamics and Quantum Chaology (Les Bouches Summer School. Session LII, 1989), M.-J. Giannoni, A. Voros and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1991), p. 547.
10. T. Takami, Phys. Rev. Lett. 68:3371 (1992).
11. H. P. Baltes, and E. R. Hilf, Spectra of Finite Systems (BI Wissenschaftsverlag, Mannheim, 1976).
12. H.-D. Gröf, H. L. Harney, H. Lengeler, C. H. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt, and H. A. Weidenmüller, Phys. Rev. Lett. 69:1296 (1992).
13. M. Sieber, U. Smilansky, S. C. Creagh, and R. G. Littlejohn, J. Phys. A: Math. Gen. 26:6217 (1993).
14. E. B. Bogomolny, Physica D 31:169 (1988).
15. S. W. McDonald and A. N. Kaufman, Phys. Rev. A 37:3067 (1988).
16. Y. Shimizu and A. Shudo, Prog. Theor. Phys. Suppl. 116:267 (1994).
17. P. Seba, Phys. Rev. Lett. 64:1855 (1990).
18. T. Shigehara, Phys. Rev. E 50:4357 (1994).
19. A. Shudo and Y. Shimizu, Statistical properties of eigen-functions for quantum billiards with and without positive exponent, to be published.