Skip to main content
Log in

The dynamics of coherent wave packets in a medium with memory

  • Elementary Physicochemical Processes
  • Published:
Russian Journal of Physical Chemistry B Aims and scope Submit manuscript

Abstract

Two qualitatively different approaches to the description of the dynamics of vibrational wave packets, with and without (Markovian approximation) taking into account memory of relaxation processes, were compared for a model molecular system with one vibrational degree of freedom (a Morse oscillator) in a medium. The master equation for the density matrix of the molecular system obtained using the Nakajima-Zwanzig formalism was used. The time evolutions of the autocorrelation function, vibrational level populations, and mean vibrational wave packet energies were calculated. At short times, taking memory effects into account could cause significant quantitative and sometimes qualitative differences in the evolution of vibrational wave packets calculated in the Markovian approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. M. Sarkisov and S. Ya. Umanskii, Usp. Khim. 70, 515 (2001).

    Google Scholar 

  2. R. N. Zare, Science 279, 1875 (1998).

    Article  CAS  Google Scholar 

  3. A. H. Zewail, Femtochemistry: Ultrafast Dynamics of the Chemical Bond (World Sci., Singapore, 1994).

    Google Scholar 

  4. E. V. Sundstrom, Femtochemistry and Femtobiology (Imperial College, London, 1997).

    Google Scholar 

  5. M. Shapiro and P. Brumer, Phys. Rep. 425, 195 (2006).

    Article  CAS  Google Scholar 

  6. M. Shapiro and P. Brumer, Rep. Prog. Phys. 66, 859 (2003).

    Article  CAS  Google Scholar 

  7. L. Van Dao, C. Lincoln, M. Lowe, and P. Hannaford, J. Chem. Phys. 120, 18 (2004).

    Article  Google Scholar 

  8. U. Fano, Rev. Mod. Phys. 29, 1 (1957).

    Article  Google Scholar 

  9. R. P. Feynman and F. L. Vernon, Jr., Ann. Phys. (N.Y.) 24, 118 (1963).

    Article  Google Scholar 

  10. U. Weiss, Quantum Dissipative Systems (World Sci., Singapore, 1993).

    Google Scholar 

  11. S. Nakajima, Prog. Theor. Phys. 20, 948 (1958).

    Article  Google Scholar 

  12. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960).

    Article  CAS  Google Scholar 

  13. R. Zwanzig, Lectures in Theoretical Physics (Interscience, New York, 1961), Vol. 3.

    Google Scholar 

  14. S. Nielsen, R. Kapral, and G. Cinotti, J. Chem. Phys. 112, 6543 (2000).

    Article  CAS  Google Scholar 

  15. A. G. Redfield, Adv. Magn. Reson. 1, 1 (1965).

    Google Scholar 

  16. F. Haake, Springer Tracts Mod. Phys. 66, 98 (1973).

    Article  Google Scholar 

  17. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Relativistic Quantum Theory (Pergamon, Oxford, 1971; Parts 1 and 2, Nauka, Moscow, 1968, 1971).

    Google Scholar 

  18. N. Makri and D. E. Makarov, Chem. Phys. Lett. 221,48 (1994).

    Google Scholar 

  19. A. J. Leggett, S. Chakravarty, A. T. Dorsey, et al., Rev. Mod. Phys. 59, 1 (1987).

    Article  CAS  Google Scholar 

  20. H. Grabert, P. Schramm, and G. Ingold, Phys. Rep. 168, 115 (1988).

    Article  CAS  Google Scholar 

  21. B. B. Laird, J. Budimir, and J. Skinner, J. Chem. Phys. 94, 4391 (1991).

    Article  CAS  Google Scholar 

  22. N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4600 (1995).

    Article  CAS  Google Scholar 

  23. N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4611 (1995).

    Article  CAS  Google Scholar 

  24. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North Holland, Amsterdam, 1981; Vysshaya Shkola, Moscow, 1986).

    Google Scholar 

  25. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II, Springer Series in Solid State Physics (Springer, Heidelberg, 1985).

    Google Scholar 

  26. M. Shugard, J. Tully, and A. Nizan, J. Chem. Phys. 69, 336 (1978).

    Article  CAS  Google Scholar 

  27. C. Meier and D. J. Tannor, J. Chem. Phys. 111, 3365 (1997).

    Article  Google Scholar 

  28. Y. Tanimura and P. G. Wolynes, J. Chem. Phys. 96, 8485 (1992).

    Article  CAS  Google Scholar 

  29. T. User and M. S. Child, Mol. Phys. 41, 1177 (1980).

    Article  Google Scholar 

  30. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. A. Rok.

Additional information

Original Russian Text © A.S. Moskalenko, D.A. Rok, S.Ya. Umanskii, 2010, published in Khimicheskaya Fizika, 2010, Vol. 29, No. 10, pp. 3–13.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moskalenko, A.S., Rok, D.A. & Umanskii, S.Y. The dynamics of coherent wave packets in a medium with memory. Russ. J. Phys. Chem. B 4, 695–704 (2010). https://doi.org/10.1134/S1990793110050015

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990793110050015

Keywords

Navigation