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A Classical and Quantum Theory of Dynamical Self-Trapping in Nonlinear Systems and its Implication to Energy Transfer in Biological Systems

  • Shozo Takeno
Part of the NATO ASI Series book series (NSSB, volume 243)

Abstract

Dynamical self-trapping of waves or particles, originally put forward by Landau long time ago, by their nonlinear self-interactions in classical and quantum systems has received much attention in recent years. The principal reason for the upsurge of the renewed interest is due to: (i) The development of the soliton theory in mathematical physics. (ii) Ever-lasting interest in Davydov solitons and their possible implication to biological energy transfer.1 (iii) Generalization of the concept of Davydov solitons in various directions,2 in which vibron solitons are one of such examples.3 (iv) Several experiments which can be accounted for by the concept of the dynamical self-trapping, such as the shift of the infrared absorption spectra of molecular crystals acetanilide,4 local modes in benzene,5 the anomalous temperature dependence of the Raman spectra in ℓ-alanine,6 and so on. (v) Numerical experiments which show the existence of dynamical self-trapped states under certain conditions in various model dynamical nonlinear systems.79 (vi) Elucidation of the existence of intrinsic an-harmonic localized or resonant modes in lattice dynamics of pure crystal lattices.10,11

Keywords

Coherent State Localize Mode Acoustic Phonon Nonlinear Eigenvalue Problem Envelope Soliton 
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.
    A.S. Davydov and N.I. Kislukha, Sov. Phys.-JETP 44, 571 (1976). See, also A.S. Davydov, “Solitons in Molecular Systems”, D. Reidel Publishing Company, Dordrect, Boston, and Lancaster, (1985), and also references cited therein.Google Scholar
  2. 2.
    D.W. Brown, K. Lindenberg, and B.J. West, Phys. Rev. A33, 4104 (1986)MathSciNetADSGoogle Scholar
  3. D.W. Brown, B.J. West, and K. Lindenberg, Phys. Rev. A33, 4110 (1988)MathSciNetADSGoogle Scholar
  4. Xidi Wang, D.W. Brown, K. Lindenberg, and B.J. West, Phys. Rev. A37, 3557 (1988).ADSGoogle Scholar
  5. 3.
    S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984), 73, 853, (1985); 75, 1 (1986).ADSCrossRefGoogle Scholar
  6. 4.
    G. Careri, U. Buontempo, F. Carta, E. Gratton, and A.C. Scott, Phys. Rev. Lett. 51, 304(1983)ADSCrossRefGoogle Scholar
  7. G. Careri, U. Buontempo, F. Galluzzi, A.C. Scott, E. Gratton, and E. Shyamsunder, Phys. Rev. B30, 4689 (1984).ADSGoogle Scholar
  8. 5.
    R.H. Page, Y.R. Shen, and Y.T. Lee, Phys. Rev. Lett., 59, 1293 (1987).ADSCrossRefGoogle Scholar
  9. 6.
    A. Migliori, P.M. Maxton, A.M. Clogston, E. Zirngiebl, and M. Lowe, Phys. Rev. B38, 13464 (1988).ADSGoogle Scholar
  10. 7.
    A.C. Scott, Phys. Scr. 29, 279 (1984)ADSCrossRefGoogle Scholar
  11. L. MacNeil and A.C. Scott, Phys, Scr. 29, 284 (1984).ADSCrossRefGoogle Scholar
  12. 8.
    P.S. Lomdahl and W.C. Kerr, Phys. Rev. Lett., 55, 1235 (1985); in Physics of Many Particle Systems, edited by A.S. Davydov, Naukova Dumka, Kiev (1988).ADSCrossRefGoogle Scholar
  13. 9.
    Xidi Wang, D.W. Brown, and K. Lindenberg, Phys. Rev. Lett., 62, 1796 (1989).ADSCrossRefGoogle Scholar
  14. 10.
    A.J. Sievers and S. Takeno, Phys. Rev. Lett., 61, 970 (1988)ADSCrossRefGoogle Scholar
  15. S. Takeno, Prog. Thoer. Phys. Suppl. No.94, 242 (1988).Google Scholar
  16. 11.
    S. Takeno and A.J. Siever, Solid State Commun., 67, 1023 (1989).ADSCrossRefGoogle Scholar
  17. 12.
    V.E. Zakharov, Sov. Phys.-JETP 35, 908 (1972).ADSGoogle Scholar
  18. 13.
    L.D. Landau, Phys. Zeit. Sowjetunion, 3, 664 (1933).zbMATHGoogle Scholar
  19. 14.
    S. Takeno, J. Phys. Soc. Jpn., 58, 759 (1989).MathSciNetADSCrossRefGoogle Scholar
  20. 15.
    M.J. Ablowitz and J.F. Ladik, J. Math. Phys., 17, 1011 (1976).MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 16.
    S. Takeno, Submitted to J. Phys. Soc. Jpn.Google Scholar
  22. 17.
    S. Takeno, J. Phys. Soc. Jpn., 57, 675 (1988).ADSCrossRefGoogle Scholar
  23. 18.
    Xidi Wang, D.W. Brown, and K. Lindenberg, Phys. Rev. B39, 5366 (1989).ADSGoogle Scholar
  24. 19.
    S. Takeno, J. Phys. Soc. Jpn., 58, 1639 (1989).MathSciNetADSCrossRefGoogle Scholar
  25. 20.
    See, for example, W.H. Louisell, “Quantum Statistical Properties of Radiation”, John Wiley & Sons, New York, London, Sydney and Toronto, (1973), p. 324.Google Scholar
  26. 21.
    S. Takeno and M. Mabuchi, Prog. Theor. Phys., 50, 1848 (1973).ADSCrossRefGoogle Scholar
  27. 22.
    P.W. Anderson, “Concepts in Solids”, W.A. Benjamin, Inc., New York and Amsterdam, (1963), p. 132.Google Scholar
  28. 23.
    J.M. Radcliffe, J. Phys. A4, 313 (1971).MathSciNetADSGoogle Scholar
  29. 24.
    F.T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A6, 2211 (1972).ADSGoogle Scholar
  30. 25.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963).MathSciNetADSCrossRefGoogle Scholar
  31. 26.
    S. Takeno, J. Phys. Soc. Jpn., 48, 1075 (1980)MathSciNetADSCrossRefGoogle Scholar
  32. 27.
    For Boson systems, see for example, J.S. Langer, Phys. Rev. 167, 183 (1968).ADSCrossRefGoogle Scholar
  33. 28.
    See also, S. Takeno and S. Homma, J. Phys. Soc. Jpn., 49, 1671 (1980).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Shozo Takeno
    • 1
  1. 1.Physics Laboratory, Faculty of Engineering and DesignKyoto Institute of TechnologyKyoto 606Japan

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