Molecular spectra, quantum chaos, and scars

European Physical Journal D

Volumn 4, Issue 2, 1998, Pages 181-187

  Arranz, F J ^a   Borondo, F ^a   Benito, R M ^b  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR SPECTROSCOPY; QUANTUM CHAOS; QUANTUM THEORY;

ATOMIC SYSTEM; CHAOTICS; LOWER RESOLUTION; MOLECULAR SPECTRA; MOLECULAR SYSTEMS; PERIODIC MOTION; PROJECTION TECHNIQUES; QUANTUM CHAOS; QUANTUM LEVELS;

MASS SPECTROMETRY;

EID: 0002146997     PISSN: 14346060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100530050198     Document Type: Article

References (57)

1. R. Schienke, Photodissociation Dynamics (Cambridge University Press, Cambridge, 1992).
2. G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, Princeton, 1964).
3. R.M. Stratt, N.C. Handy, W.H. Miller, J. Chem. Phys. 71, 3311 (1979).
4. V.B. Chirikov, Phys. Rep. 52, 263 (1979).
5. C. Jaffé, P. Bramer, J. Chem. Phys. 73, 5646 (1980);
6. E.L. Sibert III, W.P. Reinhardt, J.T. Hynes, J. Chem. Phys. 77, 3583 (1982).
7. N. De Leon, M.J. Davis, E.J. Heller, J. Chem. Phys. 80, 794 (1984).
8. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
9. L.E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, New York, 1992).
10. T. Uzer, Phys. Rep. 199, 75 (1991);
11. S.A. Schofield, P.G. Wolynes, R.E. Wyatt, Phys. Rev. Lett. 74, 3720 (1995).
12. Laser Spectroscopy of Highly Vibrationally Excited Molecules, edited by V.S. Letokhov (Adams Hilger, New York, 1989).
13. Molecular Dynamics and Spectroscopy by SEP, edited by H.L. Dai, R.W. Field (World Scientific, Singapore, 1995).
14. E.J. Heller, J. Chem. Phys. 62, 1544 (1975);
15. Chaos and Quantum Physics, edited by M. Giannoni, A. Voros, J. Zinn-Justin (Eisevier, Amsterdam, 1991).
16. C. Leforestier, R. Bisseling, C. Cerjan, M.D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.D. Meyer, N. Lipkin, O. Roncero, R. Kossloff, J. Comput. Phys. 94, 59 (1991).
17. Z. Bačić, J. Light, Ann. Rev. Phys. Chem. 40, 469 (1989).
18. D.T. Colbert, E.L. Sibert III, J. Chem. Phys. 91, 350 (1989).
19. H. Goldstein, Classical Mechanics (Addisom-Wesley, Reading, 1980).
20. M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990);
21. K. Nakamura, Quantum Chaos. A New Paradigm of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1993).
22. E.N. Lorenz, The Essence of Chaos (University College London Press, London, 1995).
23. E.J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
24. S.W. McDonald, A.N. Kaufmann, Phys. Rev. Lett. 42, 1189 (1979);
25. Phys. Rev. A 37, 3067 (1988).
26. M.V. Berry, J. Phys. A 10, 2083 (1977);
27. A. Voros, in Stochastic Behaviour in Classical and Quantum Hamiltonian Systems, edited by G. Casati, J. Ford (Springer, Berlin, 1979).
28. A.I. Shnirelman, Ups. Mat. Nauk. 29, 181 (1974).
29. M.C. Gutzwiller, J. Math. Phys. 12, 343 (1971);
30. Phys. Rev. Lett. 45, 150 (1980).
31. E.B. Bogomolny, Physica D 31, 169 (1988).
32. G.G. de Polavieja, F. Borondo, R.M. Benito, Phys. Rev. Lett. 73, 1613 (1994).
33. F.J. Arranz, F. Borondo, R.M. Benito, Phys. Rev. Lett. 80, 944 (1998).
34. P. Leboeuf, A. Voros, J. Phys. A 23, 1765 (1990);
35. M.B. Cibils, Y. Cuche, P. Leboeuf, W.F. Wreszinski, Phys. Rev. A 46, 4560 (1992).
36. K. Husimi, Proc. Phys. Soc. Jpn 22, 264 (1940).
37. F.J. Arranz, F. Borondo, R.M. Benito, Phys. Rev. E 54, 2458 (1996);
38. J. Mol. Struct. (THEOCHEM) 426, 87 (1998).
39. G. Tanner, P. Scherer, E.B. Bogomolny, B. Eckhardt, D. Wintgen, Phys. Rev. Lett. 67, 2410 (1991).
40. M.A. Iken, F. Borondo, R.M. Benito, T. Uzer, Phys. Rev. A 49, 2734 (1994).
41. Remember the Fourier transform relation existing between spectrum and correlation function (see Eq. (8) in Sect. 2 below.)
42. J.M. Gomez-Llorente, E. Pollak, Ann. Rev. Phys. Chem. 43, 91 (1992);
43. H.S. Taylor, Acc. Chem. Res. 22, 263 (1989).
44. J.M. Gomez-Llorente, N. Berenger, F. Borondo, R.M. Benito, Chem. Phys. Lett. 192, 430 (1992).
45. F. Borondo, R.M. Benito, Frontiers of Chemical Dynamics, NATO ASI Ser. C, edited by E. Yurtsever (Kluwer, Dordrecht, 1995) and references therein.
46. R. Essers, J. Tennyson, P.E.S. Wormer, Chem. Phys. Lett. 89, 223 (1982).
47. J. Makarewitz, T. Ha, J. Molec. Struct. (THEOCHEM) 315, 149 (1994);
48. Chem. Phys. Lett. 232, 497 (1995).
49. F. Borondo, A.A. Zembekov, R.M. Benito Chem. Phys. Lett. 246, 421 (1995);
50. J. Chem. Phys. 105, 5068 (1996);
51. J. Chem. Phys. ibid. 107, 7934 (1997).
52. R.M. Benito, F. Borondo, J.-H. Kim, B.G. Sumpter, G.S. Ezra, Chem. Phys. Lett. 161, 60 (1989).
53. Z. Bačić, J. Light, J. Chem. Phys. 85, 4594 (1986).
54. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vettering, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1986).
55. Although the range spanned by the angular variable θ goes from 0 to π we use for the regular states the notation corresponding to a harmonic description, in which the quantum bending number corresponds to double the number of nodes in θ. The quantum number can only be even due to the fact that we are only considering states with total angular momentum equal to zero (J = 0). See discussion in I.N. Levine, Molecular Spectroscopy (Wiley, New York, 1975), p. 271.
56. W.H. Miller, J. Chem. Phys. 72, 99 (1980).
57. W.P. Reinhardt, C. Jaffé, Quantum Mechanics in Mathematics, Chemistry and Physics, edited by K.E. Gustavson, W.P. Reinhardt (Plenum, New York, 1981).