Temperature Effects on the Davydov Soliton

  • H. Bolterauer
Part of the NATO ASI Series book series (NSSB, volume 243)


There are two effects which tend to delocalize the Davydov soliton. First, quantum fluctuations which can also be seen as a zero point motion of the soliton position. Second, thermal fluctuations produced by the interaction with the surrounding solvent. This solvent, which we now call heatbath, wants to force the system into thermal equilibrium. We discuss under what circumstances a soliton in the Alpha-helix can be seen as a thermodynamic equilibrium state. We show how the principle of a minimal free energy, formulated in a variational principle of thermodynamics, can be used to optimize a given ansatz for the density operator. Thermal soliton theories of Davydov and Krumhansl are discussed within this theory. Both, in principle, use the same ansatz with no freedom to adjust for maximum entropy. In using a more realistic ansatz, we always get the result that the soliton is delocalized. Finally, we discuss how the strength of interaction, together with the internal structure of the heatbath, determines the thermal lifetime of the soliton.


Quantum State Variational Principle Thermal Equilibrium Density Operator Canonical Ensemble 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Davydov, A.S., J. Theor. Biol. 38 (1973) 559.CrossRefGoogle Scholar
  2. 2.
    Davydov, A.S. and Kislukha, N.I., Phys. Stat. Sol. B59 (1973).Google Scholar
  3. 3.
    See Davydov, A.S., Solitons in Molecular Systems, Riedel, Dordrecht (1985) for bibliographies.Google Scholar
  4. 4.
    Scott, A.C., Phys. Rev. A26 (1982) 578.ADSGoogle Scholar
  5. 5.
    Scott, A.C., Phys. Scripta 25 (1982) 651MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    MacNeil, L. and Scott, A.C. Phys. Scripta 29 (1984) 284ADSCrossRefGoogle Scholar
  7. 7.
    Bolterauer, H. and Henkel, R.D., Phys. Scripta T13 (1986) 314ADSCrossRefGoogle Scholar
  8. 8.
    Lomdahl, P.S. and Kerr, W.C., Phys. Rev. Lett. 55 (1985) 1235ADSCrossRefGoogle Scholar
  9. 9.
    Lawrence, A.F., McDaniel, J.C., Chang, D.B., Pierce, B. M. and Birge, R.R., Phys. Rev. A33 (1986) 1188ADSGoogle Scholar
  10. 10.
    Scott, A.C., “On Davydov Solitons at 310 K”, in Energy Transfer Dynamics edited by T. W. Barett and H. A. Pohl; Springer-Verlag 1987Google Scholar
  11. 11.
    Bolterauer, H., “Aspects of Quantum Mechanical Thermalisation in the Alpha-Helix”, in Structure, Coherence and Chaos in Dynamical Systems, edited by P. L. Christiansen and R. D. Parmentier, Manchester University Press 1986.Google Scholar
  12. 12.
    Bolterauer, H. and Opper, M. “The Quantum lifetime of the Davydov solitonr; submitted to Physica Scripta November 1988Google Scholar
  13. 13.
    Brown, B.W., Lindenberg, K. and West, B.J., Phys. Rev. A33 (1986) 4104MathSciNetADSGoogle Scholar
  14. 14.
    Davydov, A.S., Phys. stat. sol. B138 (1986) 559ADSGoogle Scholar
  15. 15.
    Cruzeiro, L., Halding, J., Christiansen, P.L., Skovgaard, O. and Scott, A.C., Phys. Rev. A37, 880 (1988)ADSGoogle Scholar
  16. 16.
    Kadantzev, V.N., Lupichov, L.N. and Savin, A.V., Phys. stat. sol.(b) 143, 569 (1987) and Phys. stat. sol.(b) 147, 155 (1988)ADSCrossRefGoogle Scholar
  17. 17.
    Alexander, D.M. and Krumhansl, J.A., Phys. Rev. B33 (1986) 7172ADSGoogle Scholar
  18. 18.
    Brown, D.W., Lindenberg, K. and West, B.J., Phys. Rev A33, 4110 (1986)MathSciNetADSGoogle Scholar
  19. 19.
    Brown, D.W., Lindenberg, K. and West, B.J., Phys. Rev A33, 4114 (1986)ADSGoogle Scholar
  20. 20.
    Venzl, G. and Fischer, F., J. Chem. Phys. 81, 6090 (1984)ADSCrossRefGoogle Scholar
  21. 21.
    Venzl, G. and Fischer, F., J. Phys. Rev. B32, 6437 (1985)ADSGoogle Scholar
  22. 22.
    Cottingham, J. P. and Schweitzer, J. W., Phys. Ref. Lett. 62, 1792 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    Bolterauer, H., “Quantum effects on the Davydov soliton” this VolumeGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • H. Bolterauer
    • 1
  1. 1.Institut für Theoretische PhysikJustus-Liebig-Universität GiessenGiessenGermany

Personalised recommendations