Semiclassical quantization of chaos in terms of an amplitude-free quasi-correlation function

Journal of Physics A: Mathematical and General

Volumn 36, Issue 17, 2003, Pages 4785-4803

  Hotta, Koji ^a   Takatsuka, Kazuo ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038061658     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/17/306     Document Type: Article

References (52)

1. Tabor M 1989 Chaos and Integrability in Nonlinear Dynamics (New York: Wiley) Reichl L E 1992 The Transition to Chaos (New York: Springer) Nakamura K 1993 Quantum Chaos (Cambridge: Cambridge University Press) Gaspard P 1993 Chaos, Scattering and Statistical Mechanics (Cambridge: Cambridge University Press)
2. Tabor M 1989 Chaos and Integrability in Nonlinear Dynamics (New York: Wiley) Reichl L E 1992 The Transition to Chaos (New York: Springer) Nakamura K 1993 Quantum Chaos (Cambridge: Cambridge University Press) Gaspard P 1993 Chaos, Scattering and Statistical Mechanics (Cambridge: Cambridge University Press)
3. Tabor M 1989 Chaos and Integrability in Nonlinear Dynamics (New York: Wiley) Reichl L E 1992 The Transition to Chaos (New York: Springer) Nakamura K 1993 Quantum Chaos (Cambridge: Cambridge University Press) Gaspard P 1993 Chaos, Scattering and Statistical Mechanics (Cambridge: Cambridge University Press)
4. Tabor M 1989 Chaos and Integrability in Nonlinear Dynamics (New York: Wiley) Reichl L E 1992 The Transition to Chaos (New York: Springer) Nakamura K 1993 Quantum Chaos (Cambridge: Cambridge University Press) Gaspard P 1993 Chaos, Scattering and Statistical Mechanics (Cambridge: Cambridge University Press)
5. Berggren K-F and Åberg S (ed) 2001 Quantum Chaos Y2K Physica Scripta (Stockholm, Sweden: The Royal Swedish Academy of Sciences)
6. Gutzwiller M C 1970 J. Math. Phys. 11 1791 Gutzwiller M C 1971 J. Math. Phys. 12 343 Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (Berlin: Springer)
7. Gutzwiller M C 1970 J. Math. Phys. 11 1791 Gutzwiller M C 1971 J. Math. Phys. 12 343 Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (Berlin: Springer)
8. Gutzwiller M C 1970 J. Math. Phys. 11 1791 Gutzwiller M C 1971 J. Math. Phys. 12 343 Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (Berlin: Springer)
9. Voros A 1988 J. Phys. A: Math. Gen. 21 685
10. Berry M V and Keating J P 1990 J. Phys. A: Math. Gen. 23 4839 Berry M V and Keating J P 1992 Proc. R. Soc. A 437 151
11. Berry M V and Keating J P 1990 J. Phys. A: Math. Gen. 23 4839 Berry M V and Keating J P 1992 Proc. R. Soc. A 437 151
12. Vergini E and Wisniacki D A 1998 Phys. Rev. E 58 R5225 Vergini E G 2000 J. Phys. A: Math. Gen. 33 4709
13. Vergini E and Wisniacki D A 1998 Phys. Rev. E 58 R5225 Vergini E G 2000 J. Phys. A: Math. Gen. 33 4709
14. Miller W H 1970 J. Chem. Phys. 53 3578
15. Heller E J 1991 J. Chem. Phys. 94 2723
16. Sepúlveda M A and Heller E J 1994 J. Chem. Phys. 101 8004 Sepúlveda M A and Grossmann F 1996 Adv. Chem. Phys. 96 191
17. Sepúlveda M A and Heller E J 1994 J. Chem. Phys. 101 8004 Sepúlveda M A and Grossmann F 1996 Adv. Chem. Phys. 96 191
18. Campolieti G and Brumer P 1994 Phys. Rev. A 50 997 Provost D and Brumer P 1995 Phys. Rev. Lett. 74 250
19. Campolieti G and Brumer P 1994 Phys. Rev. A 50 997 Provost D and Brumer P 1995 Phys. Rev. Lett. 74 250
20. Kay K G 1994 J. Chem. Phys. 100 4377 Kay K G 1994 J. Chem. Phys. 100 4432 Kay K G 1994 J. Chem. Phys. 101 2250
21. Kay K G 1994 J. Chem. Phys. 100 4377 Kay K G 1994 J. Chem. Phys. 100 4432 Kay K G 1994 J. Chem. Phys. 101 2250
22. Kay K G 1994 J. Chem. Phys. 100 4377 Kay K G 1994 J. Chem. Phys. 100 4432 Kay K G 1994 J. Chem. Phys. 101 2250
23. Miller W H 1974 Adv. Chem. Phys. 25 69 Schulman L S 1981 Techniques and Applications of Path Integration (New York: Wiley) Gaspard P, Alonso D and Burghardt I 1995 Adv. Chem. Phys. 90 105
24. Miller W H 1974 Adv. Chem. Phys. 25 69 Schulman L S 1981 Techniques and Applications of Path Integration (New York: Wiley) Gaspard P, Alonso D and Burghardt I 1995 Adv. Chem. Phys. 90 105
25. Miller W H 1974 Adv. Chem. Phys. 25 69 Schulman L S 1981 Techniques and Applications of Path Integration (New York: Wiley) Gaspard P, Alonso D and Burghardt I 1995 Adv. Chem. Phys. 90 105
26. Inoue-Ushiyama A and Takatsuka K 2001 Phys. Rev. E 64 056223
27. Hinde R J, Berry R S and Wales D J 1992 J. Chem. Phys. 96 1376 Hinde R J and Berry R S 1993 J. Chem. Phys. 99 2942
28. Hinde R J, Berry R S and Wales D J 1992 J. Chem. Phys. 96 1376 Hinde R J and Berry R S 1993 J. Chem. Phys. 99 2942
29. Takatsuka K 2001 Phys. Rev. E 64 016224
30. Takatsuka K and Inoue A 1997 Phys. Rev. Lett. 78 1404 Inoue-Ushiyama A and Takatsuka K 1999 Phys. Rev. A 59 3256 Inoue-Ushiyama A and Takatsuka K 1999 Phys. Rev. A 60 112
31. Takatsuka K and Inoue A 1997 Phys. Rev. Lett. 78 1404 Inoue-Ushiyama A and Takatsuka K 1999 Phys. Rev. A 59 3256 Inoue-Ushiyama A and Takatsuka K 1999 Phys. Rev. A 60 112
32. Takatsuka K and Inoue A 1997 Phys. Rev. Lett. 78 1404 Inoue-Ushiyama A and Takatsuka K 1999 Phys. Rev. A 59 3256 Inoue-Ushiyama A and Takatsuka K 1999 Phys. Rev. A 60 112
33. Goldstein H 1980 Classical Mechanics (New York: Addison-Wesley)
34. Miller W H 1974 Adv. Chem. Phys. 25 69
35. Shao J and Makri N 1999 J. Phys. Chem. A 103 7753 Shao J and Makri N 1999 J. Phys. Chem. A 103 9479
36. Shao J and Makri N 1999 J. Phys. Chem. A 103 7753 Shao J and Makri N 1999 J. Phys. Chem. A 103 9479
37. Hashimoto N and Takatsuka K 1995 J. Chem. Phys. 103 6914
38. Kosloff D and Kosloff R 1983 J. Comput. Phys. 52 35
39. Yoshida H 1990 Phys. Lett. A 150 262 Takahashi K and Ikeda K 1993 J. Chem. Phys. 99 8680
40. Yoshida H 1990 Phys. Lett. A 150 262 Takahashi K and Ikeda K 1993 J. Chem. Phys. 99 8680
41. Jaffé C and Reinhardt W P 1982 J. Chem. Phys. 77 5191 Shirts R B and Reinhardt W P 1982 J. Chem. Phys. 77 5204
42. Jaffé C and Reinhardt W P 1982 J. Chem. Phys. 77 5191 Shirts R B and Reinhardt W P 1982 J. Chem. Phys. 77 5204
43. Noid D W and Marcus R A 1975 J. Chem. Phys. 62 2119 Swimm R T and Delos J B 1979 J. Chem. Phys. 71 1706 Skodje R T, Borondo F and Reinhardt W P 1985 J. Chem. Phys. 82 4611 Sholberg K and Shirts R B 1994 J. Chem. Phys. 101 7763 Sohlberg K, Tuzun R E, Sumpter B G and Noid D W 1998 Phys. Rev. A 57 906
44. Noid D W and Marcus R A 1975 J. Chem. Phys. 62 2119 Swimm R T and Delos J B 1979 J. Chem. Phys. 71 1706 Skodje R T, Borondo F and Reinhardt W P 1985 J. Chem. Phys. 82 4611 Sholberg K and Shirts R B 1994 J. Chem. Phys. 101 7763 Sohlberg K, Tuzun R E, Sumpter B G and Noid D W 1998 Phys. Rev. A 57 906
45. Noid D W and Marcus R A 1975 J. Chem. Phys. 62 2119 Swimm R T and Delos J B 1979 J. Chem. Phys. 71 1706 Skodje R T, Borondo F and Reinhardt W P 1985 J. Chem. Phys. 82 4611 Sholberg K and Shirts R B 1994 J. Chem. Phys. 101 7763 Sohlberg K, Tuzun R E, Sumpter B G and Noid D W 1998 Phys. Rev. A 57 906
46. Noid D W and Marcus R A 1975 J. Chem. Phys. 62 2119 Swimm R T and Delos J B 1979 J. Chem. Phys. 71 1706 Skodje R T, Borondo F and Reinhardt W P 1985 J. Chem. Phys. 82 4611 Sholberg K and Shirts R B 1994 J. Chem. Phys. 101 7763 Sohlberg K, Tuzun R E, Sumpter B G and Noid D W 1998 Phys. Rev. A 57 906
47. Noid D W and Marcus R A 1975 J. Chem. Phys. 62 2119 Swimm R T and Delos J B 1979 J. Chem. Phys. 71 1706 Skodje R T, Borondo F and Reinhardt W P 1985 J. Chem. Phys. 82 4611 Sholberg K and Shirts R B 1994 J. Chem. Phys. 101 7763 Sohlberg K, Tuzun R E, Sumpter B G and Noid D W 1998 Phys. Rev. A 57 906
48. A crucial argument on this matter is given in Tomsovic S and Heller E J 1991 Phys. Rev. Lett. 67 664
49. Ushiyama H, Arasaki Y and Takatsuka K 2001 Chem. Phys. Lett. 346 169
50. Takatsuka K, Ushiyama H and Inoue-Ushiyama A 1999 Phys. Rep. 322 347
51. Takahashi S and Takatsuka K in preparation
52. Hotta K, Takahashi S and Takatsuka K unpublished