Experimental versus numerical eigenvalues of a Bunimovich stadium billiard: A comparison

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

Volumn 60, Issue 3, 1999, Pages 2851-2857

  Alt, H ^a   Dembowski, C ^a   Graf H D ^a   Hofferbert, R ^a   Rehfeld, H ^a   Richter, A ^a,b   Schmit, C ^c  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b Wissenschaftskolleg zu Berlin   (Germany)

^c 91405 Orsay Campus   (France)

Author keywords

[No Author keywords available]

Indexed keywords

REVIEW;

EID: 4243989355     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.2851     Document Type: Article

References (33)

1. M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1980).
2. S.W. McDonald and A.N. Kaufman, Phys. Rev. Lett. 42, 1189 (1979).
3. M.V. Berry, Proc. R. Soc. London, Ser. A 413, 183 (1987).
4. M.L. Mehta, Random Matrices and the Statistical Theories of Energy Levels, 2nd ed. (Academic Press, San Diego, 1991).
5. O. Bohigas, in Chaos and Quantum Physics, edited by A. Veros, and J. Zinn-Justin, M.-J. Giannoni (Elsevier, Amsterdam, 1991), p. 89.
6. S. Sridhar, Phys. Rev. Lett. 67, 785 (1991).
7. H.-J. Stöckmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990)
8. Phys. Rev. Lett.J. Stein and H.-J. Stöckmann, 68, 2867 (1992).
9. H.-D. Gräf, H.L. Harney, H. Lengeler, C.H. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt, and H.A. Weidenmüller, Phys. Rev. Lett. 69, 1296 (1992).
10. L.A. Bunimovich, Funct. Anal. Appl. 8, 254 (1974)
11. L.A. BunimovichCommun. Math. Phys. 65, 295 (1985)
12. L.A. BunimovichZh. Éksp. Teor. Fiz. 89, 1452 (1985) [Sov. Phys. JETP 62, 842 (1985)].
13. D. Alonso and P. Gaspard, J. Phys. A 27, 1599 (1994).
14. E.B. Bogomolny, Physica D 31, 169 (1988).
15. H. Alt, C. Dembowski, H.-D. Gräf, T. Guhr, R. Hofferbert, H. Rehfeld, A. Richter, R. Schuhmann, and T. Weiland, Phys. Rev. Lett. 79, 1026 (1997).
16. H. Alt, C.I. Barbosa, H.-D. Gräf, T. Guhr, H.L. Harney, R. Hofferbert, H. Rehfeld, and A. Richter, Phys. Rev. Lett. 81, 4847 (1998).
17. H. Alt, H.-D. Gräf, H.L. Harney, R. Hofferbert, H. Lengeler, A. Richter, P. Schardt, and H.A. Weidenmüller, Phys. Rev. Lett. 74, 62 (1995).
18. H. Alt, P. v. Brentano, H.-D. Gräf, R.-D. Herzberg, M. Phillip, A. Richter, and P. Schardt, Nucl. Phys. A 560, 293 (1993).
19. H. Alt, P. v. Brentano, H.-D. Gräf, R. Hofferbert, M. Phillip, H. Rehfeld, A. Richter, and P. Schardt, Phys. Lett. B 366, 7 (1996).
20. M. Sieber and F. Steiner, Phys. Lett. A 148, 415 (1990).
21. H. Weyl, J. Reine Angew. Math. Band 141, 1 (1912)
22. J. Reine Angew. Math. BandH. Weyl141, 163 (1912).
23. H. Weyl, J. Reine Angew. Math. Band 143, 177 (1913).
24. H.P. Baltes and E.R. Hilf, Spectra of Finite Systems (Bibliographisches Institut, Mannheim, 1975).
25. O. Bohigas and M.-J. Giannoni, in Mathematical and Computional Methods in Nuclear Physics, edited by J.S. Dehesa, J.M.G. Gomez, and A. Polls, Lecture Notes in Physics Vol. 209 (Springer, Berlin, 1984), p. 1.
26. F.J. Dyson and M.L. Mehta, J. Math. Phys. 4, 701 (1963).
27. M.V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984).
28. M. Sieber, U. Smilansky, S.C. Creagh, and R.G. Littlejohn, J. Phys. A 26, 6217 (1993).
29. M.V. Berry, Proc. R. Soc. London, Ser. A 400, 229 (1985).
30. This, however, was not completely possible—as can be seen from the remnants of the lowest bbo in Fig. 66 at (Formula presented) m—due to the numerical uncertainties when Eq. (18) is applied to the data.
31. H.D. Erfling, Ann. Phys. (N.Y.) 41, 467 (1942).
32. A. Shudo and Y. Shimizu, Phys. Rev. A 42, 6264 (1990).
33. G. Benettin and J.-M. Strelcyn, Phys. Rev. A 17, 773 (1978).