Smoothed density of states for problems with ray splitting

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

Volumn 53, Issue 1, 1996, Pages 207-213

  Prange, R E ^a   Ott, Edward ^a   Antonsen, T M ^a   Georgeot, Bertrand ^a   Blümel, Reinhold ^a  

^a University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000299187     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.207     Document Type: Article

References (20)

1. L. Couchman, E. Ott and T. M. Antonsen, Jr., , Phys. Rev. A 46, 6193 (1992).
2. R. N. Oerter, E. Ott, T. M. Antonsen, Jr., and P. So (unpublished).
3. R. Blümel, T. M. Antonsen, Jr., B. Georgeot, E. Ott, and R. E. Prange (unpublished).
4. A. M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, Cambridge, 1988).
5. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, Berlin, 1990).
6. E. Ott, Chaos in Dyanmical Systems (Cambridge University Press, Cambridge, 1993), Chap. 10.
7. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) 60, 401 (1970);
8. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) 63, 592 (1971);
9. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) 64, 271 (1971).
10. D. J. Vasil'ev, Trans. Moscow Math. Soc. 49, 173 (1987).
11. This paper's result also includes the possibility of ray splitting although the situation studied does not apply to any of the cases we consider [e.g., Fig. 1(a)].
12. See also M. Sieber, H. Primack, U. Smilansky, I. Ussishkin, and H. Schanz (unpublished).
13. For example, H.-J. Stockmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990);
14. S. Sridhar, Phys. Rev. Lett. 67, 785 (1991);
15. H. D. Graf , Phys. Rev. Lett. 69, 1296 (1992);
16. P. So, S. M. Anlage, E. Ott and R. N. Oerter, Phys. Rev. Lett. 74, 2662 (1995).
17. The situation in Fig. 1(c) can also be treated by summing four contributions of the form of (8) corresponding to the four reflection coefficients, one for S waves incident from x < 0 converted to reflected S waves in x < 0 and similar reflection coefficients for P waves incident from x < 0, S waves incident from x > 0, and P waves incident from x > 0.
18. Quantum chaos experiments in elastic media have recently been done [R. L. Weaver, J. Acoust. Soc. Am. 85, 1001 (1989);
19. D. Delande, D. Sornette and R. Weaver, J. Acoust. Soc. Am. 93, 1873 (1994);
20. C. Ellegard , Phys. Rev. Lett. 75, 1546 (1996)].