Advertisement

JETP Letters

, Volume 86, Issue 3, pp 221–224 | Cite as

Loschmidt echo and the stochastic quantum dynamics of nanoparticles

  • V. A. Benderskii
  • L. A. Falkovsky
  • E. I. Kats
Miscellaneous

Abstract

The time evolution of a prepared vibrational state (system) coupled to a reservoir with a dense spectrum of its vibrational states has been investigated under the assumption that the reservoir has an equidistant spectrum, and the system-reservoir coupling matrix elements are independent of the reservoir states. The analytical solution manifests three regimes of the evolution for the system: (i) weakly damped oscillations; (ii) a multicomponent Loschmidt echo in recurrence cycles; and (iii) overlapping recurrence cycles. We find the characteristic critical values of the system-reservoir coupling constant for the transitions between these regimes. Stochastic dynamics occurs in regime (iii) due to an unavoidably, in any real system, coarse graining of the time or energy measurements or the initial condition uncertainty. At any finite accuracy, one can always find the cycle number k c when the dynamics of the system for k>k c cannot be determined uniquely from the spectrum, and, in this sense, the long-time system evolution becomes chaotic. Even though a specific toy model is investigated here, when properly interpreted, it yields quite a reasonable description for a variety of physically relevant phenomena, such as the complex vibrational dynamics of nanoparticles with characteristic interlevel spacing on the order of 10 cm−1 observed using subpicosecond spectroscopy methods.

PACS numbers

05.45.-a 72.10.-d 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Ben-Num, F. Molnar, H. Lu, et al., Faraday Discuss. 110, 447 (1998).CrossRefGoogle Scholar
  2. 2.
    W. Fuss, W. E. Schmidt, and S. A. Trushin, J. Chem. Phys. 112, 8347 (2000).CrossRefADSGoogle Scholar
  3. 3.
    M. Joeux, S. C. Farantos, and R. Schinke, J. Phys. Chem. A 106, 5407 (2002).Google Scholar
  4. 4.
    C. J. Fecko, J. D. Eaves, J. J. Loparo, et al., Science 301, 1698 (2003).CrossRefADSGoogle Scholar
  5. 5.
    A. J. Leggett, S. Chakravarty, A. T. Dorsey, et al., Rev. Mod. Phys. 59, 1 (1987).CrossRefADSGoogle Scholar
  6. 6.
    V. A. Benderskii, D. E. Makarov, and C. A. Wight, Chemical Dynamics at Low Temperatures (Wiley, New York, 1994).Google Scholar
  7. 7.
    U. Weiss, quantum Dissipative Systems, 2nd ed. (World Sci., Singapore, 1999).Google Scholar
  8. 8.
    M. L. Mehta, Random Matrices (Academic, New York, 1968).Google Scholar
  9. 9.
    R. Zwanzig, Lect. Theor. Phys. 3, 106 (1960).Google Scholar
  10. 10.
    Higher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdelyi (McGraw-Hill, New York, 1953; Nauka, Moscow, 1974), Vol. 2.Google Scholar
  11. 11.
    Ya. B. Zeldovich, JETP 12, 542 (1961).Google Scholar
  12. 12.
    G. M. Zaslavsky, Chaos in Dynamical Systems (Nauka, Moscow, 1984; Harwood, New York, 1985).Google Scholar
  13. 13.
    M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989; Éditorial URSS, Moscow, 2000).MATHGoogle Scholar
  14. 14.
    M. Bixon and J. Jortner, J. Chem. Phys. 48, 715 (1968); J. Chem. Phys. 107, 1470 (1997).CrossRefGoogle Scholar
  15. 15.
    V. A. Benderskii and E. I. Kats, Phys. Rev. E 65, 036217 (2002).Google Scholar
  16. 16.
    P. Grigolini, Quantum Mechanical Irreversibility (World Sci., Singapore, 1993).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • V. A. Benderskii
    • 1
  • L. A. Falkovsky
    • 2
    • 3
  • E. I. Kats
    • 2
    • 4
    • 3
  1. 1.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Institute for High Pressure PhysicsRussian Academy of SciencesTroitsk, Moscow regionRussia
  4. 4.Institut Laue-LangevinGrenobleFrance

Personalised recommendations