Dynamical tunneling in mixed systems

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

Volumn 57, Issue 2, 1998, Pages 1421-1443

  Frischat, S D ^a   Doron, E ^a  

^a MAX PLANCK INSTITUT FÜR KERNPHYSIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0343861171     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.1421     Document Type: Article

References (69)

1. O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rev. Lett. 65, 5 (1990)
2. A. Einstein, Verh. Deut. Phys. Ges. 19, 82 (1917); VDPEAZ
3. L. Brillouin, J. Phys. Radium 7, 353 (1926); JPRAAJ
4. J. B. Keller, Ann. Phys. (N.Y.) 4, 180 (1958).
5. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1990).
6. W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927 (1990); PRLTAO
7. W. A. LinL. E. BallentinePhys. Rev. A 45, 3637 (1992);
8. A. Peres, Phys. Rev. Lett. 67, 158 (1991)
9. O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rep. 223, 43 (1993)
10. R. Utermann, T. Dittrich, and P. Hänggi, Phys. Rev. E 49, 273 (1994).
11. O. Bohigas, D. Boosé, R. Egydio de Carvallho, and V. Marvulle, Nucl. Phys. A 560, 197 (1993)
12. S. Tomsovic and D. Ullmo, Phys. Rev. E 50, 145 (1994).
13. F. Leyvraz and D. Ullmo, J. Phys. A 10, 2529 (1996).
14. E. Doron and S. D. Frischat, Phys. Rev. Lett. 75, 3661 (1995)
15. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).
16. E. P. Wigner, Phys. Rev. 40, 749 (1932); PHRVAO
17. M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984)
18. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940); PPMJAJ
19. K. Takahashi, Prog. Theor. Phys. Suppl. 98, 109 (1989)
20. E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984)
21. D. W. Noid and R. A. Marcus, J. Chem. Phys. 67, 559 (1977).
22. O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rev. Lett. 64, 1479 (1990)
23. V. P. Maslov, The Perturbation Series and Asymptotic Methods (Moscow University, Moscow, 1965).
24. M. Wilkinson, Physica D 21, 341 (1986); PDNPDT
25. M. Wilkinson, J. Phys. A 20, 635 (1987); JPHAC5
26. S. C. Creagh and N. D. Whelan, Phys. Rev. Lett. 77, 4975 (1996)
27. W. H. Miller and T. F. George, J. Chem. Phys. 56, 5668 (1972); JCPSA6
28. W. H. MillerT. F. GeorgeAdv. Chem. Phys. 25, 69 (1974).
29. W. H. Miller, Adv. Chem. Phys. 30, 77 (1975)
30. M. J. Davis and E. J. Heller, J. Chem. Phys. 75, 246 (1981).
31. G. Casati, R. Graham, I. Guarneri, and F. M. Izrailev, Phys. Lett. A 190, 159 (1994)
32. S. D. Frischat and E. Doron, J. Phys. A 30, 3613 (1997).
33. O. Bohigas, in Proceedings of the 1989 Les Houches Summer School on “Chaos and Quantum Physics,” edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier Science Publishers B.V., Amsterdam, 1991), p. 547.
34. A. Richter, in Proceedings of the Workshop on Emerging Applications of Number Theory (University of Minnesota, Minneapolis, 1996).
35. E. Doron and U. Smilansky, Nonlinearity 5, 1055 (1992).
36. E. B. Bogomolny, Nonlinearity 5, 805 (1992).
37. R. Blümel and U. Smilansky, Phys. Rev. Lett. 64, 241 (1990)
38. M. V. Berry and K. E. Mount, Rep. Prog. Phys. 35, 315 (1972)
39. S. D. Frischat, Ph.D. thesis, Heidelberg University, 1996 (unpublished).
40. E. Doron and S. D. Frischat (unpublished).
41. W. Franz, Z. Naturforsch. 9, 705 (1954).
42. J. B. Keller, J. Opt. Soc. Am. 52, 116 (1962)
43. G. Hackenbroich, E. Narimanov, and A. D. Stone, Phys. Rev. E (to be published).
44. R. S. MacKay, J. D. Meiss, and I. C. Percival, Phys. Rev. Lett. 52, 697 (1984); PRLTAO
45. R. S. MacKayJ. D. MeissI. C. PercivalPhysica D 13, 55 (1984).
46. R. T. Swimm and J. B. Delos, J. Chem. Phys. 71, 1706 (1979).
47. O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984)
48. R. Blümel and U. Smilansky, Phys. Rev. Lett. 60, 477 (1988)
49. F. J. Dyson, J. Math. Phys. 3, 140 (1962)
50. P. Gerwinsiki and P. Šeba, Phys. Rev. E 50, 3615 (1994).
51. D. Klakow and U. Smilansky, J. Phys. A 29, 3213 (1996).
52. H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (BI Wissenschaftsverlag, Mannheim, 1978).
53. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, San Diego, 1965).
54. We thank Felix von Oppen for contributing the main idea for this calculation.
55. R. Hofferbert, Master Thesis, Technische Hochschule Darmstadt, 1994.
56. H. Friedrich and D. Wintgen, Phys. Rep. 183, 37 (1989); PRPLCM
57. D. Delande, in Proceedings of the 1989 Les Houches Summer School on “Chaos and Quantum Physics,” edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier Science Publishers B.V., Amsterdam, 1991), p. 665.
58. D. Wintgen, K. Richter, and G. Tanner, Chaos 2, 19 (1991); CHAOEH
59. K. Richter, J. S. Briggs, D. Wintgen, and E. A. Solov’ev, J. Phys. B 25, 3929 (1992)
60. F. L. Moore, Phys. Rev. Lett. 75, 4598 (1995)
61. V. Averbukh, N. Moiseyev, B. Mirbach, and H. J. Korsch, Z. Phys. D 35, 247 (1995).
62. J. U. Nöckel, A. D. Stone, and R. K. Chang, Opt. Lett. 19, 1693 (1994); OPLEDP
63. A. Mekis, Phys. Rev. Lett. 75, 2682 (1995); PRLTAO
64. J. U. Nöckel and A. D. Stone, Nature (London) 385, 45 (1997)
65. G. Hackenbroich and J. U. Nöckel, Europhys. Lett. 39, 371 (1997)
66. J. Zakrzewski, D. Delande, and A. Buchleitner, Phys. Rev. E (to be published).
67. S. Tomsovic, M. Grinberg, and D. Ullmo, Phys. Rev. Lett. 75, 4346 (1995); PRLTAO
68. D. Ullmo, M. Grinberg, and S. Tomosovic, Phys. Rev. E 54, 136 (1996).
69. K. M. Frahm and D. L. Shepelyansky, Phys. Rev. Lett. 78, 1440 (1997). PRLTAO