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Volumn 113, Issue 7, 2000, Pages 2741-2759

Properties of random state manifolds with applications to intramolecular vibrational redistribution

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRONIC DENSITY OF STATES; ITERATIVE METHODS; MATHEMATICAL MODELS; MOLECULAR STRUCTURE; MOLECULAR VIBRATIONS; MONTE CARLO METHODS; PERTURBATION TECHNIQUES; POISSON DISTRIBUTION; RANDOM PROCESSES;

EID: 0034250070     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1305526     Document Type: Article
Times cited : (13)

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    • Zimmermann, Th.1    Köppel, H.2    Cederbaum, L.S.3
  • 68
    • 0000589459 scopus 로고
    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1989) Ann. Phys. (N.Y.) , vol.193 , pp. 472
    • Guhr, T.1    Weidenmüller, H.A.2
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    • 0000266185 scopus 로고
    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1992) Phys. Rev. Lett. , vol.70 , pp. 572
    • Alhassid, Y.1    Whelan, N.2
  • 70
    • 0000906369 scopus 로고
    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 529
    • Benet, L.1    Seligman, T.H.2    Weidenmüller, H.A.3
  • 71
    • 21844495162 scopus 로고
    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1995) J. Phys. Soc. Jpn. , vol.64 , pp. 4059
    • Ma, J.-Z.1
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    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1995) Nucl. Phys. B , vol.453 , pp. 531
    • Brézin, E.1    Zee, A.2
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    • 0007073949 scopus 로고    scopus 로고
    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1997) Nuovo Cimento Soc. Ital. Fis. B , vol.112 B , pp. 543
    • Mezzadri, F.1    Scotti, A.2
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    • 0031556977 scopus 로고    scopus 로고
    • See for example: T. H. Seligman, J. J. M. Verbaarschot, and M. R. Zirnbauer, Phys. Rev. Lett. 53, 215 (1984); M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); T. S. Ishikawa and T. Yukawa, Phys. Rev. Lett. 54, 1617 (1985); Th. Zimmermann, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 91, 3934 (1989); T. Guhr and H. A. Weidenmüller, Ann. Phys. (N.Y.) 193, 472 (1989); Y. Alhassid and N. Whelan, Phys. Rev. Lett. 70, 572 (1992); L. Benet, T. H. Seligman, and H. A. Weidenmüller, ibid. 71, 529 (1993); J.-Z. Ma, J. Phys. Soc. Jpn. 64, 4059 (1995); E. Brézin and A. Zee, Nucl. Phys. B 453, 531 (1995); F. Mezzadri and A. Scotti, Nuovo Cimento Soc. Ital. Fis. B, 112B, 543 (1997); Guozhen Wu, Chem. Phys. Lett. 265, 449 (1997).
    • (1997) Chem. Phys. Lett. , vol.265 , pp. 449
    • Wu, G.1
  • 80
    • 0007120939 scopus 로고    scopus 로고
    • note
    • l))].
  • 81
    • 0007022721 scopus 로고    scopus 로고
    • note
    • ls are not numbered with increasing size.
  • 82
    • 0003632783 scopus 로고
    • edited by W. Ledermann, Probability Wiley, New York
    • Emlyn Lloyd, in Handbook of Applicable Mathematics, edited by W. Ledermann, Vol. II: Probability (Wiley, New York, 1980).
    • (1980) Handbook of Applicable Mathematics , vol.2
    • Lloyd, E.1
  • 83
    • 0003930336 scopus 로고
    • North-Holland, Amsterdam, Appendix A.
    • A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1964), Appendix A. Eq. (A18).
    • (1964) Quantum Mechanics
    • Messiah, A.1
  • 84
    • 0004245694 scopus 로고
    • edited by M. Abramowitz and I. A. Stegun Dover, New York.
    • Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York. 1970).
    • (1970) Handbook of Mathematical Functions
  • 85
    • 0007134431 scopus 로고    scopus 로고
    • l alone
    • l alone.
  • 86
    • 0007032973 scopus 로고    scopus 로고
    • note
    • l, and Eq. (3.30) is not ρW(0.0) then. The final result for the DOS, Eq. (3.32), nevertheless holds for this case also.
  • 88
    • 26644456508 scopus 로고
    • Wahrscheinlichkeitsrechnung und Mathematische Statistik, edited by H. Grell, K. Maruhn, und W. Rinow (VEB Deutscher Verlag der Wissenschaften, Berlin), Eq. (6.12.3)
    • M. Fisz, in Wahrscheinlichkeitsrechnung und Mathematische Statistik, Hochschulbücher für Mathematik, Bd. 40, edited by H. Grell, K. Maruhn, und W. Rinow (VEB Deutscher Verlag der Wissenschaften, Berlin, 1980), Eq. (6.12.3).
    • (1980) Hochschulbücher für Mathematik , vol.40
    • Fisz, M.1
  • 91
    • 0007029302 scopus 로고    scopus 로고
    • note
    • 54 Taken from the density of vibrational states of symmetry Γ. The degree of degeneracy was dropped due to the separation of different components of degenerate bright states caused by the totally symmetric vibrational Hamiltonian.
  • 96
    • 0004172950 scopus 로고
    • Collier-MacMillan, London, Secs. 8.3 and 8.5
    • R. H. Pennington, Introductory Computer Methods and Numerical Analysis (Collier-MacMillan, London, 1970), Secs. 8.3 and 8.5; J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1993), Secs. 5.1 and 5.6.
    • (1970) Introductory Computer Methods and Numerical Analysis
    • Pennington, R.H.1
  • 97
    • 0003882610 scopus 로고
    • Springer, New York, Secs. 5.1 and 5.6
    • R. H. Pennington, Introductory Computer Methods and Numerical Analysis (Collier-MacMillan, London, 1970), Secs. 8.3 and 8.5; J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1993), Secs. 5.1 and 5.6.
    • (1993) Introduction to Numerical Analysis
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  • 129
    • 0037781267 scopus 로고
    • N.Y.
    • See for example: H. Feshbach, Ann. Phys. (N.Y.) 43, 410 (1967);
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    • Feshbach, H.1
  • 143
  • 208
    • 26644475274 scopus 로고    scopus 로고
    • note
    • 4))].
  • 209
    • 26644458187 scopus 로고    scopus 로고
    • note
    • ls are not numbered with increasing size.
  • 210
    • 0003632783 scopus 로고
    • edited by W. Ledermann, Probability Wiley, New York
    • Emlyn Lloyd, in Handbook of Applicable Mathematics, edited by W. Ledermann, Vol. II: Probability (Wiley, New York, 1980).
    • (1980) Handbook of Applicable Mathematics , vol.2
    • Lloyd, E.1
  • 211
    • 0003930336 scopus 로고
    • North-Holland, Amsterdam, Appendix A, Eq.
    • A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1964), Appendix A, Eq. (A18).
    • (1964) Quantum Mechanics
    • Messiah, A.1
  • 213
    • 26644451917 scopus 로고    scopus 로고
    • note
    • l alone.
  • 214
    • 26644442633 scopus 로고    scopus 로고
    • note
    • l, and Eq. (3.30) is not ρW(0,0) then. The final result for the DOS, Eq. (3.32), nevertheless holds for this case also.
  • 216
    • 26644456508 scopus 로고
    • Wahrscheinlichkeitsrechnung und Mathematische Statistik, edited by H. Grell, K. Maruhn, und W. Rinow VEB Deutscher Verlag der Wissenschaften, Berlin, Eq. (6.12.3)
    • M. Fisz, in Wahrscheinlichkeitsrechnung und Mathematische Statistik, Hochschulbücher für Mathematik, Bd. 40, edited by H. Grell, K. Maruhn, und W. Rinow (VEB Deutscher Verlag der Wissenschaften, Berlin, 1980), Eq. (6.12.3).
    • (1980) Hochschulbücher für Mathematik , vol.40
    • Fisz, M.1
  • 219
    • 26644465823 scopus 로고    scopus 로고
    • note
    • Taken from the density of vibrational states of symmetry Γ. The degree of degeneracy was dropped due to the separation of different components of degenerate bright states caused by the totally symmetric vibrational Hamiltonian.


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