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Harmonic inversion of time signals and its applications

J. Chem. Phys. 107, 6756 (1997); doi:10.1063/1.475324

Issue Date: 1 November 1997 | See: Erratum

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Vladimir A. Mandelshtam and Howard S. Taylor
Department of Chemistry, University of Southern California, Los Angeles, California 90089
New methods of high resolution spectral analysis of short time signals are presented. These methods utilize the filter-diagonalization approach of Wall and Neuhauser [J. Chem. Phys. 102, 8011 (1995)] that extracts the complex frequencies omegak and amplitudes dk from a signal C(t)=[summation]kdke–itomegak in a small frequency interval by recasting the harmonic inversion problem as the one of a small matrix diagonalization. The present methods are rigorously adapted to the conventional case of the signal available on a sparse equidistant time grid and use a more efficient boxlike filter. Various applications are discussed, such as iterative diagonalization of large Hamiltonian matrices for calculating bound and resonance states, scattering calculations in the presence of narrow resonances, etc. For the scattering problem the harmonic inversion is directly applied to the signal cn=(chif,Tn(H)chii), generated by the dynamical system governed by a modified Chebyshev recursion, avoiding the usual recasting the problem to the time domain. Some challenging numerical examples are presented. The general filter-diagonalization method is shown to be stable and efficient for the extraction of thousands of complex frequencies omegak and amplitudes dk from a signal. When the model signal is "spoiled" by a moderate amount of an additive Gaussian noise the obtained spectral estimate is still superior to the conventional Fourier spectrum. ©1997 American Institute of Physics.
History: Received 7 May 1997; accepted 28 July 1997
Permalink: http://link.aip.org/link/?JCPSA6/107/6756/1
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ERRATUM

  1. Erratum: "Harmonic inversion of time signals and its applications" [J. Chem. Phys. 107, 6756 (1997)]
    Vladimir A. Mandelshtam et al.
    J. Chem. Phys. 109, 4128 (1998)

KEYWORDS and PACS

Keywords
PACS
  • 31.90.+s
    Electronic structure of atoms, molecules and their ions: theory Other topics in the theory of the electronic structure of atoms, molecules, and their ions
  • 33.15.Mt
    Molecular properties and interactions with photons Properties of molecules and molecular ions Rotation, vibration, and vibrationrotation constants
  • 33.20.Tp
    Molecular properties and interactions with photons Molecular spectra Vibrational analysis
  • 31.50.+w
    Electronic structure of atoms, molecules and their ions: theory Excited states
  • 03.65.Ge
    Classical and quantum physics: mechanics and fields Quantum mechanics Solutions of wave equations: bound states
  • YEAR: 1996-97

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
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REFERENCES (43)
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For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. D. J. Tannor and D. E. Weeks, J. Chem. Phys. 98, 3884 (1993);
    2. D. E. Weeks and D. J. Tannor, Chem. Phys. Lett. 207, 301 (1993).
  2. W. Zhu, J. Dai, J. Z. H. Zhang, and D. H. Zhang, J. Chem. Phys. 105, 4881 (1996).
  3. M. D. Feit and J. A. Fleck, J. Chem. Phys. 78, 301 (1983).
  4. H. Tal-Ezer and R. Kosloff, J. Chem. Phys. 81, 3967 (1984).
  5. R. Kosloff, Annu. Rev. Phys. Chem. 45, 145 (1994).
  6. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 103, 2903 (1995);
    7. V. A. Mandelshtam, "Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular physics," edited by D. G. Truhlar, and B. Simon, IMA Volumes in Mathematics and its Applications (1996), Vol. 89, p. 389.
  7. M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984);
    8. E. Kluk, M. F. Herman, and H. L. Davis, J. Chem. Phys. 84, 326 (1986);
    M. A. Sepuálveda and F. Grossmann, Adv. Chem. Phys. XCVI, 191 (1996);
    K. G. Kay, J. Chem. Phys. 100, 4377 (1994);
    100, 4432 (1994);
    G. Campolieti and P. Brumer, Phys. Rev. A 50, 997 (1994);
    A. R. Walton and D. E. Manolopoulos, Mol. Phys. 87, 961 (1996);
    B. W. Spath and W. H. Miller, J. Chem. Phys. 104, 95 (1996).
  8. R. Roy, B. G. Sumpter, D. W. Noid, and B. Wunderlich, J. Phys. Chem. 94, 5720 (1990).
  9. S. Marple, Jr., Digital Spectral Analysis with Applications (Prentice-Hall, Englewood Cliffs, NJ, 1987).
  10. R. Roy, B. G. Sumpter, G. A. Pfeffer, S. K. Gray, and D. W. Noid, Comput. Phys. Rep. 205, 109 (1991).
  11. S. K. Gray, J. Chem. Phys. 96, 6543 (1992).
  12. M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995).
  13. D. Neuhauser, J. Chem. Phys. 93, 2611 (1990).
  14. N. Moiseyev, P. R. Certain, and F. Weinhild, Mol. Phys. 36, 1613 (1978).
  15. G.-J. Kroes, M. R. Wall, J. W. Pang, and D. Neuhauser, J. Chem. Phys. 106, 1800 (1997).
  16. J. W. Pang and D. Neuhauser, Chem. Phys. Lett. 252, 173 (1996).
  17. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 106, 5085 (1997).
  18. V. A. Mandelshtam and H. S. Taylor, Phys. Rev. Lett. 78, 3274 (1997).
  19. J. Main, V. A. Mandelshtam, and H. S. Taylor, Phys. Rev. Lett. 79, 825 (1997).
  20. J. Main, V. A. Mandelshtam, and H. S. Taylor, Phys. Rev. Lett. 78, 4351 (1997).
  21. F. Grossmann, V. A. Mandelshtam, H. S. Taylor, and J. S. Briggs, Chem. Phys. Lett. (in press).
  22. C. Lanczos, Applied Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1956).
  23. W. Zhu, Y. Huang, D. J. Kouri, C. Chandler, and D. K. Hoffman, Chem. Phys. Lett. 217, 73 (1994).
  24. R. Chen and H. Guo, J. Chem. Phys. 105, 3569 (1996).
  25. R. N. Silver and H. Röder, Int. J. Mod. Phys. C 5, 735 (1994);
    26. R. N. Silver, H. Röder, A. F. Voter, and J. D. Kres, J. Comput. Phys. 124, 115 (1996);
    L. W. Wang, Phys. Rev. B 49, 10154 (1994).
  26. H. Röder, H. Fehshke, and R. N. Silver, Europhys. Lett. 28, 250 (1996).
  27. L. W. Wang, Phys. Rev. Lett. 73, 1039 (1994).
  28. S. Goedecker and L. Colombo, Phys. Rev. Lett. 73, 122 (1994);
    29. A. F. Voter, J. D. Kres, and R. N. Silver, Phys. Rev. B 53, 12753 (1996).
  29. R. N. Silver, H. Röder, A. F. Voter, and J. D. Kres, in Maximum Entropy and Bayesian Methods 1995, edited by K. Hanson and R. N. Silver (Kluwer Academic, Dordrecht, 1995);
    30. R. N. Silver and H. Röder, Phys. Rev. E (submitted).
  30. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 102, 7390 (1995).
  31. P.-N. Roy and T. Carrington, Jr., J. Chem. Phys. 103, 5600 (1995);
    32. D. J. Kouri, W. Zhu, G. Parker, and D. K. Hoffman, Chem. Phys. Lett. 238, 395 (1995);
    R. Chen and H. Guo, J. Chem. Phys. 105, 1311 (1996);
    R. Baer, Y. Zeiri, and R. Kosloff, Phys. Rev. B 54, 5287 (1996).
  32. T. P. Grozdanov, V. A. Mandelshtam, and H. S. Taylor, J. Chem. Phys. 103, 7990 (1995);
    33. V. A. Mandelshtam, T. P. Grozdanov, and H. S. Taylor, ibid. 103, 10074 (1995).
  33. V. A. Mandelshtam and H. S. Taylor, J. Chem. Soc. Faraday Trans. 93, 847 (1997).
  34. J. Aguilar and J. M. Combes, Commun. Math. Phys. 22, 269 (1971);
    35. E. Baslev and J. E. Combas, ibid. 22, 280 (1971);
    B. Simon, Ann. Math. 97, 247 (1973);
    N. Moiseyev, Isr. J. Chem. 31, 311 (1991).
  35. G. Jolicard and E. J. Austin, Chem. Phys. Lett. 121, 106 (1985);
    36. Chem. Phys. 103, 295 (1986);
    G. Jolicard, C. Leforestier, and E. J. Austin, J. Chem. Phys. 88, 1026 (1988).
  36. D. Wang and J. M. Bowman, J. Chem. Phys. 100, 1021 (1994).
  37. C. Leforestier, K. Yamashita, and N. Moiseyev, J. Chem. Phys. 103, 8468 (1995).
  38. B. Hartke, R. Kosloff, and S. Ruhman, Chem. Phys. Lett. 158, 238 (1989);
    39. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).
  39. Y. Huang, W. Zhu, D. J. Kouri, and D. K. Hoffman, Chem. Phys. Lett. 206, 96 (1993).
  40. D. J. Kouri, Y. Huang, W. Zhu, and D. K. Hoffman, J. Chem. Phys. 100, 3662 (1994).
  41. M. J. Bramley, J. W. Tromp, T. Carrington, Jr., and B. T. Sutcliffe, J. Chem. Phys. 98, 10104 (1993).
  42. All the numerical results mentioned are available electronically by request. E-mail: mandelsh[chem1. usc. edu
  43. R. Chen and H. Guo (preprint).

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