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Propagation of excitation in long 1D chains: Transition from regular quantum dynamics to stochastic dynamics

  • V. A. Benderskii
  • E. I. Kats
Atoms, Molecules, Optics

Abstract

The quantum dynamics problem for a 1D chain consisting of 2N + 1 sites (N ≫ 1) with the interaction of nearest neighbors and an impurity site at the middle differing in energy and in coupling constant from the sites of the remaining chain is solved analytically. The initial excitation of the impurity is accompanied by the propagation of excitation over the chain sites and with the emergence of Loschmidt echo (partial restoration of the impurity site population) in the recurrence cycles with a period proportional to N. The echo consists of the main (most intense) component modulated by damped oscillations. The intensity of oscillations increases with increasing cycle number and matrix element C of the interaction of the impurity site n = 0 with sites n = ±1 (0 < C ≤ 1; for the remaining neighboring sites, the matrix element is equal to unity). Mixing of the components of echo from neighboring cycles induces a transition from the regular to stochastic evolution. In the regular evolution region, the wave packet propagates over the chain at a nearly constant group velocity, embracing a number of sites varying periodically with time. In the stochastic regime, the excitation is distributed over a number of sites close to 2N, with the populations varying irregularly with time. The model explains qualitatively the experimental data on ballistic propagation of the vibrational energy in linear chains of CH2 fragments and predicts the possibility of a nondissipative energy transfer between reaction centers associated with such chains.

Keywords

Wave Packet Secular Equation Partial Amplitude Impurity Site Laguerre Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. User and W. H. Miller, Phys. Rep. 199, 73 (1991).ADSCrossRefGoogle Scholar
  2. 2.
    V. M. Kenkre, A. Tokmakoff, and M. D. Fayer, J. Chem. Phys. 101, 10618 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, Oxford, 1995).Google Scholar
  4. 4.
    C. J. Fesko, J. D. Eaves, J. J. Loparo, A. Tokmakoff, and P. L. Geissler, Science (Wasington) 301, 1698 (2003).ADSCrossRefGoogle Scholar
  5. 5.
    D. M. Leitner, Adv. Chem. Phys. B 130, 205 (2005).CrossRefGoogle Scholar
  6. 6.
    R. Zwanzig, Lect. Theor. Phys. 3, 106 (1960).Google Scholar
  7. 7.
    V. A. Benderskii, L. A. Falkovsky, and E. I. Kats, JETP Lett. 86(3), 221 (2007).ADSCrossRefGoogle Scholar
  8. 8.
    V. A. Benderskii and E. I. Kats, JETP Lett. 88(5), 338 (2008).ADSCrossRefGoogle Scholar
  9. 9.
    V. A. Benderskii, L. N. Gak, and E. I. Kats, JETP 108(1), 159 (2009); V. A. Benderskii, L. N. Gak, and E. I. Kats, JETP 109 (3), 505 (2009).ADSCrossRefGoogle Scholar
  10. 10.
    V. A. Benderskii and E. I. Kats, JETP Lett. 92(6), 370 (2010).ADSCrossRefGoogle Scholar
  11. 11.
    R. G. Snyder, J. Chem. Phys. 47, 1316 (1967).ADSCrossRefGoogle Scholar
  12. 12.
    T. Ishioka, W. Yan, H. L. Strauss, and R. G. Snyder, Spectrochim. Acta, Part A 59, 671 (2003).ADSCrossRefGoogle Scholar
  13. 13.
    K. R. Rodriguez, S. Shah, S. M. Williams, S. Teeters- Kennedy, and J. V. Coe, J. Chem. Phys. 121, 8671 (2004).ADSCrossRefGoogle Scholar
  14. 14.
    H. Kuzmany, B. Burger, A. Thess, and R. E. Smalley, Carbon 36, 709 (1998).CrossRefGoogle Scholar
  15. 15.
    O. P. Charkin and N. M. Klimenko, private communication (2009).Google Scholar
  16. 16.
    O. P. Charkin, N. M. Klimenko, and D. O. Charkin, Adv. Quantum Chem. 56, 69 (2009).CrossRefGoogle Scholar
  17. 17.
    M. Ben-Nun, F. Molnar, H. Lu, J. C. Phillips, T. J. Martinez, and K. Schulten, Faraday Discuss. 110, 447 (1998).ADSCrossRefGoogle Scholar
  18. 18.
    S. Hayashi, E. Tajkhorshid, and K. Schulten, Biophys. J. 85, 1440 (2003).CrossRefGoogle Scholar
  19. 19.
    G. K. Paramonov, H. Naundorf, and O. Kuhn, Eur. J. Phys. D 14, 205 (2001).ADSCrossRefGoogle Scholar
  20. 20.
    H. Fujisaki, Y. Zhang, and J. E. Straub, J. Chem. Phys. 124, 14491 (2006).CrossRefGoogle Scholar
  21. 21.
    S. Spörlein, H. Carstens, H. Satzger, C. Renner, R. Behrendt, L. Moroder, P. Tavan, W. Zinth, and J. Wachtveitl, Proc. Natl. Acad. Sci. USA 99, 7998 (2002).ADSCrossRefGoogle Scholar
  22. 22.
    J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, J. Am. Chem. Soc. 130, 2152 (2008).CrossRefGoogle Scholar
  23. 23.
    J. A. Carter, Z. Wang, and D. D. Dlott, Acc. Chem. Res. 42, 1343 (2009).CrossRefGoogle Scholar
  24. 24.
    I. V. Rubtsov, Acc. Chem. Res. 42, 1385 (2009).CrossRefGoogle Scholar
  25. 25.
    C. Keating, B. A. McClure, J. J. Rack, and I. V. Rubtsov, J. Chem. Phys. 133, 144513 (2010).ADSCrossRefGoogle Scholar
  26. 26.
    Z. Lin, P. Keiffer, and I. V. Rubtsov, J. Phys. Chem. B 115, 5347 (2011).CrossRefGoogle Scholar
  27. 27.
    M. Galperin, M. A. Ratner, and A. Nitzan, J. Phys.: Condens. Matter 19, 103201 (2007).ADSCrossRefGoogle Scholar
  28. 28.
    V. A. Benderskii and E. I. Kats, JETP Lett. 94(6), 459 (2011).ADSCrossRefGoogle Scholar
  29. 29.
    P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960).MathSciNetADSzbMATHCrossRefGoogle Scholar
  30. 30.
    C. Domb, Proc. R. Soc. London, Ser. A 276, 418 (1963).ADSzbMATHCrossRefGoogle Scholar
  31. 31.
    A. S. Kovalev, Theor. Math. Phys. 37(1), 926 (1978).MathSciNetCrossRefGoogle Scholar
  32. 32.
    D. Hennig, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4550 (2000).CrossRefGoogle Scholar
  33. 33.
    Z. Lin and B. Li, J. Phys. Soc. Jpn. 76, 074003 (2008).ADSGoogle Scholar
  34. 34.
    F. R. Gantmacher and M. G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems (Gostekhizdat, Moscow, 1950; American Mathematical Society, Providence, Rhode Island, United States, 2002).Google Scholar
  35. 35.
    H. Bateman and A. Erdelyi, Higher Transcendental Functions, (McGraw Hill, New York, 1953), Vol. 2.Google Scholar
  36. 36.
    F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974).Google Scholar
  37. 37.
    G. M. Zaslavsky, Chaos in Dynamic Systems (Nauka, Moscow, 1984; Taylor and Francis, London, 1985).Google Scholar
  38. 38.
    M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, New York, 1989; URSS, Moscow, 2001).zbMATHGoogle Scholar
  39. 39.
    W. H. Zurek, Phys. Rev. D: Part. Fields 26, 1862 (1982).MathSciNetADSCrossRefGoogle Scholar
  40. 40.
    P. Grigolini, Quantum Mechanical Irreversibility (World Scientific, Singapore, 1993).CrossRefGoogle Scholar
  41. 41.
    E. Fermi, J. R. Pasta, and S. M. Ulam, Los Alamos Sci. Lab., [Rep.], No. LA-1940 (1955).Google Scholar
  42. 42.
    R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1984; Mir, Moscow, 1988).Google Scholar
  43. 43.
    R. W. Robinett, Phys. Rep. 392, 1 (2004).MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    E. B. Fel’dman, R. Brushweiler, and R. R. Ernst, Chem. Phys. Lett. 294, 297 (1998).ADSCrossRefGoogle Scholar
  45. 45.
    A. S. Davydov, Solitons in Molecular Systems (Kluwer, Dordrecht, 1985).zbMATHCrossRefGoogle Scholar
  46. 46.
    D. Hochstrasser, F. G. Mertens, and H. Buttner, Phys. Rev. A: At., Mol., Opt. Phys. 40, 2602 (1989).ADSCrossRefGoogle Scholar
  47. 47.
    A. Campa, A. Giansanti, A. Tenenbaum, D. Levi, and O. Ragnisco, Phys. Rev. B: Condens. Matter 48, 10168 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia

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