On the number of bouncing ball modes in billiards

Journal of Physics A: Mathematical and General

Volumn 30, Issue 19, 1997, Pages 6783-6795

  Backer A ^a   Schubert, R ^a   Stifter, P ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031558524     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/30/19/017     Document Type: Article

References (26)

1. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
2. Keller J B and Rubinow S I 1960 Asymptotic solution of eigenvalue problems Ann. Phys., NY 9 24-75 Keller J B and Rubinow S I 1960 Asymptotic solution of eigenvalue problems Ann. Phys., NY 10 303-5 (erratum)
3. Keller J B and Rubinow S I 1960 Asymptotic solution of eigenvalue problems Ann. Phys., NY 9 24-75 Keller J B and Rubinow S I 1960 Asymptotic solution of eigenvalue problems Ann. Phys., NY 10 303-5 (erratum)
4. McDonald S W and Kaufmann A N 1988 Wave chaos in the stadium: statistical properties of short-wave solutions of the Helmholtz equation Phys. Rev. A 37 3067-86
5. Heller E J 1984 Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits Phys. Rev. Lett. 53 1515-18
6. Bai Y Y, Hose G, Stefański K and Taylor H S 1985 Born-Oppenheimer adiabatic mechanism for regularity of states in the quantum stadium billiard Phys. Rev. A 31 2821-6
7. O'Connor P W and Heller E J 1988 Quantum localization for a strongly classically chaotic system Phys. Rev. Lett. 61 2288-91
8. Tanner G 1997 How chaotic is the stadium billiard? A semiclassical analysis J. Phys. A: Math. Gen. 30 2863-88
9. Sinai Ya G 1970 Dynamical systems with elastic reflections Russ. Math. Surv. 25 137-89
10. Bunimovich L A 1974 On ergodic properties of certain billiards Funct. Anal. Appl. 8 254-5
11. Bunimovich L A 1979 On the ergodic properties of nowhere dispersing billiards Commun. Math. Phys. 65 295-312
12. Shnirelman A I 1974 Ergodic properties of eigenfunctions Usp. Math. Nauk 29 181-2 (in Russian)
13. Shnirelman A I 1993 On the asymptotic properties of eigenfunctions in the regions of chaotic motion (addendum to V F Lazutkin) KAM Theory and Semiclassical Approximations to Eigenfunctions (Berlin: Springer)
14. Colin de Verdière Y 1985 Ergodicité et fonctions propres du laplacien Commun. Math. Phys. 102 111-34
15. Zelditch S 1987 Uniform distribution of eigenfunctions on compact hyperbolic surfaces Duke. Math. J. 55 919-41
16. Gérard P and Leichtnam E 1993 Ergodic properties of eigenfunctions for the Dirichlet problem Duke Math. J. 71 559-607
17. Zelditch S and Zworski M 1996 Ergodicity of eigenfunctions for ergodic billiards Commun. Math. Phys. 175 673-82
18. Sarnak P 1995 Arithmetic quantum chaos Isr. Math. Conf. Proc. 8 183-236
19. Landau L D and Lifshitz E M 1977 Quantum Mechanics: Non-relativistic Theory 3rd edn (Oxford: Pergamon)
20. Sieber M, Primack H, Smilansky U, Ussishkin I and Schanz H 1995 Semiclassical quantization of billiards with mixed boundary conditions J. Phys. A: Math. Gen. 28 5041-78
21. Stifter P 1996 Quantenbillards und Quantenchaos Ph D thesis Abteilung für Quantenphysik, Universität Ulm
22. Riddel J R Jr 1979 Boundary-distribution solution of the Helmholtz equation for a region with corners J. Comp. Phys. 31 21-41
23. Berry M V and Wilkinson M 1984 Diabolical points in the spectra of triangles Proc. Roy. Soc. London 392 15-43
24. Aurich R and Steiner F 1993 Statistical properties of highly excited quantum eigenstates of a strongly chaotic system Physica 64D 185-214
25. Gräf H-D, Harney H L, Lengeler H, Lewerikopf C H, Rangacharyulu C, Richter A, Schardt P and Weidenmüller H A 1992 Distribution of eigenmodes in a superconducting stadium billiard with chaotic dynamics Phys. Rev. Lett. 69 1296-9
26. Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 Non-generic spectral statistics in the quantized stadium billiard J. Phys. A: Math. Gen. 26 6217-30