Advertisement

JETP Letters

, Volume 88, Issue 5, pp 338–341 | Cite as

Nonexponential decay in the quantum dynamics of nanosystems

  • V. A. Benderskii
  • E. I. Kats
Article

Abstract

The quantum dynamical problem is solved for a system coupled to an equidistant-spectrum bath with the energy difference Ω between the neighboring levels n and n + 1 and the coupling matrix elements C n 2 = C 2(1 + Δ−2 n 2)−1 constraining the energy interval comprising the bath states interacting with the system. The evolution in the strong-coupling limit is determined by two parameters, Γ = πC 2/Ω ≫ 1 and α = Γ/Δ. If α ≠ 0, then the decrease in the population in the initial cycle with a period of 2π/Ω is not exponential and the effective rate constant increases with time. The results qualitatively explain the appearance of nonexponential relaxation regimes for a dense-spectrum nanosystem and predict the possibility of the multiple recovery of the initial-state population.

PACS numbers

03.65.-w 82.20.-w 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Weisskopf and E. P. Wigner. Z. Phys. 63, 54 (1930).CrossRefGoogle Scholar
  2. 2.
    M. Bixon and J. Jortner, Mol. Phys. 17, 109 (1969).CrossRefADSGoogle Scholar
  3. 3.
    P. Grigolini, Quantum Mechanical Irreversibility (World Scientific, Singapore, 1993).Google Scholar
  4. 4.
    A. Shimony, Conceptual Foundations of Quantum Mechanics (Cambridge Univ. Press, New York, 1993).Google Scholar
  5. 5.
    E. C. G. Sudarshan, C. B. Chiu, and G. Bhamathi, Adv. Chem. Phys. 99, 121 (1997).CrossRefGoogle Scholar
  6. 6.
    R. Zwanzig, Lectures in Theor. Phys. 3, 106 (1960).Google Scholar
  7. 7.
    V. A. Benderskii, L. A. Falkovskii, and E. I. Kats, Pis’ma Zh. Éksp. Teor. Fiz. 86, 221 (2007) [JETP Lett. 86, 221 (2007)].Google Scholar
  8. 8.
    V. A. Benderskii and E. I. Kats, Phys. Rev. E 65, 036217 (2002).Google Scholar
  9. 9.
    M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989; URSS, Moscow, 2001).MATHGoogle Scholar
  10. 10.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics (Nauka, Moscow, 1989; Pergamon, Oxford, 1977).Google Scholar
  11. 11.
    T. Petrovsky and I. Prigogine, Adv. Chem. Phys. 99, 1 (1997).CrossRefGoogle Scholar
  12. 12.
    A. I. Baz’, Ya. B. Zeldovich, and A. M. Perelomov, Scattering, Reactions and Decays in Nonrelativistic Quantum Mechanics (Nauka, Moscow, 1971, 2nd ed.; Israel Program for Scientific Translations, Jerusalem, 1966, transl. of the 1st Russ. ed.).Google Scholar
  13. 13.
    G. Breit and E. P. Wigner, Phys. Rev. 49, 519 (1936).MATHCrossRefADSGoogle Scholar
  14. 14.
    M. Ben-Num, F. Molnar, H. Lu, et al., Farad. Discuss. 110, 447 (1998).CrossRefGoogle Scholar
  15. 15.
    C. J. Fesco, J. D. Eaves, J. J. Loparo, et al., Science 301, 1698 (2003).CrossRefADSGoogle Scholar
  16. 16.
    A. V. Benderskii and K. B. Eisental, J. Phys. Chem. A 106, 7482 (2002).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • V. A. Benderskii
    • 1
  • E. I. Kats
    • 2
    • 3
  1. 1.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  3. 3.Institut Laue-LangevinGrenoble, Cedex 9France

Personalised recommendations