When Is A Soliton?

  • David W. Brown
  • Katja Lindenberg
  • Xidi Wang
Part of the NATO ASI Series book series (NSSB, volume 243)


The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell [2]. The latter article asks the question “When is a particle?” and deals with the changing standards of proof which lead us today to accept as “real” some fundamental particles (quarks) which we may never observe. Our situation is somewhat similar in that “hard evidence” of the existence of Davydov solitons remains elusive despite many years of effort expended in their study. As has been revealed during the discussions at this meeting, a part of this elusiveness does not arise from genuine problems of physics but from problems of communication between workers in the field. Among the latter is a considerable variance in the accepted meanings of the central terms “soliton” and “Davydov soliton” themselves. While most of us have a working knowledge of what the latter term means, the lack of a precise definition has been a root cause of some of the softness in the concept of the Davydov soliton. The physics of the underlying physical problem is, of course, completely indifferent to such linguistic difficulties which are purely of human origin; it is well, therefore, not to imbue them with undue importance. However, as the technical portion of this paper addresses a rather broad spectrum of behaviors open to an exciton in a deformable solid, we shall find it necessary to impose some precision on the terms to be used. In our general discussion, we will try use more general terms; when we encounter more distinct and special structures, we will try to preserve the distinctions in our language. It is inevitable that our terminology will conflict with that accepted by some segments of our audience; however, we hope that that will not prevent our message from being understood.


Soliton Solution Small Polaron Adiabatic Limit Quantum Monte Carlo Nonlinear SchrOdinger Equation 
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.
    David Böhm, Quantum Theory, (Prentice-Hall, New York, 1951).Google Scholar
  2. 2.
    Sidney Drell, Physics Today 31 No. 6, 23 (1978).CrossRefGoogle Scholar
  3. 3.
    T. D. Lee, Particle Physics and Introduction to Field Theory, Contemporary Concepts in Physics, Vol. 1, edited by H. Feshbach, N. Bloembergen, L. Kadanoff, M. Ruderman, S. B. Treiman and H. Primakoff (Harwood Academic Publishers, New York, 1988).Google Scholar
  4. 4.
    A. S. Davydov, Phys. Stat. Sol. 36, 211 (1969)ADSCrossRefGoogle Scholar
  5. A. S. Davydov and N. I. Kislukha, Phys. Stat. Sol. 59, 465 (1973); Zh. Eksp. Teor. Fiz. 71, 1090 (1976) [Sov. Phys.-JETP 44, 571 (1976)]ADSCrossRefGoogle Scholar
  6. A. S. Davydov, Phys. Scr. 20, 387 (1979).ADSzbMATHCrossRefGoogle Scholar
  7. 5.
    L. D. Landau, Phys. Zeit. Sowjetunion 3, 664 (1933)zbMATHGoogle Scholar
  8. S. I. Pekar, Zh. Eksp. Theor. Fiz. 16, 335 (1946)Google Scholar
  9. L. D. Landau and S. I. Pekar, Zh. Eksp. Teor. Fiz. 18, 419 (1948).Google Scholar
  10. 6.
    H. Fröhlich, H. Pelzer and S. Zieman, Phil. Mag. 41, 221 (1950)zbMATHGoogle Scholar
  11. H. Fröhlich, Proc. R. Soc. London Ser. A 215, 291 (1952); Adv. Phys. 3, 325 (1954).ADSzbMATHCrossRefGoogle Scholar
  12. 7.
    I. Pekar, Untersuchungen Uber die Electronentheorie der Kristalle, (Akademie Verlag, Berlin, 1954).Google Scholar
  13. 8.
    T. Holstein, Ann. Phys. (N.Y.) 8, 326 (1959).ADSGoogle Scholar
  14. 9.
    Emmanuel I. Rashba, in Excitons, edited by E. I. Rashba and M. D. Sturge (North-Holland, Amsterdam, 1982).Google Scholar
  15. 10.
    M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa and E. Hanamura, Excitonic Processes in Solids, Springer Series in Solid-State Sciences, Vol. 60 (Springer-Verlag, Berlin, 1986).CrossRefGoogle Scholar
  16. 11.
    Xidi Wang, David W. Brown, Katja Lindenberg and Bruce J. West, Phys. Rev. A 37, 3557 (1988).ADSCrossRefGoogle Scholar
  17. 12.
    David W. Brown, Katja Lindenberg and Bruce J. West, Phys. Rev. A 33, 4104 (1986); David W. Brown, Bruce J. West and Katja Lindenberg, Phys. Rev. A 33, 4110 (1986).MathSciNetADSCrossRefGoogle Scholar
  18. 13.
    A. S. Davydov, Zh. Eksp. Teor. Fiz. 51, 789 (1980) [Sov. Phys.-JETP 78, 397 (1980)].ADSGoogle Scholar
  19. 14.
    M. J. Skrinjar, D. V. Kapor and S. D. Stojanovic, Phys. Rev. A 37, 639 (1988).ADSCrossRefGoogle Scholar
  20. 15.
    David W. Brown, Bruce J. West and Katja Lindenberg, Phys. Rev. A 37, 642 (1988).ADSCrossRefGoogle Scholar
  21. 16.
    M. J. Skrinjar, D. V. Kapor and S. D. Stojanovic, Phys. Rev. A. 38, 6402 (1988).ADSCrossRefGoogle Scholar
  22. 17.
    Q. Zhang, V. Romero-Rochin and R. Silbey, Phys. Rev. A 38, 6409 (1988).ADSCrossRefGoogle Scholar
  23. 18.
    P. Langhoff, S. T. Epstein and M. Karplus, Rev. Mod. Phys. A 44, 602 (1972).MathSciNetADSCrossRefGoogle Scholar
  24. 19.
    J. Frenkel, Wave Mechanics, Advanced General Theory (Clarendon Press, Oxford, 1974).Google Scholar
  25. 20.
    Peter Kramer and Marcos Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics, Vol. 140, edited by J. Ehlers, K. Hepp, R. Kippenhahn, H. A. Weidenmüller and J. Zittartz (Springer-Verlag, New York, 1981).CrossRefGoogle Scholar
  26. 21.
    David W. Brown, Phys. Rev. A 37, 5010 (1988).MathSciNetADSCrossRefGoogle Scholar
  27. 22.
    I. G. Lang and Yu. A. Firsov Zh. Eksp. Teor. Fiz. 43, 1834 (1962).Google Scholar
  28. 23.
    T. Holstein, Ann. Phys. (N.Y.) 8, 343 (1959).ADSCrossRefGoogle Scholar
  29. 24.
    P. Ehrenfest, Z. Phys. 45, 455 (1927).ADSzbMATHCrossRefGoogle Scholar
  30. 25.
    David W. Brown and Zoran Ivic, Phys. Rev. B 40, 9876 (1989-I).ADSCrossRefGoogle Scholar
  31. 26.
    Yutaka Toyozawa, Prog. Theor. Phys. 26, 29 (1961); Yutaka Toyozawa, in Organic Molecular Aggregates, edited by P. Reineker, H. Haken and H. C. Wolf (Springer-Verlag, Berlin, 1983).MathSciNetADSzbMATHCrossRefGoogle Scholar
  32. 27.
    David Yarkony and Robert Silbey, J. Chem. Phys. 65, 1042 (1976); 67, 5818 (1977).ADSCrossRefGoogle Scholar
  33. 28.
    M. Sataric, Z. Ivic, Z. Shemsedini and R. Zakula, J. Molec. Elec. 4, 223 (1988).Google Scholar
  34. 29.
    Zoran Ivic and David W. Brown, Phys. Rev. Lett. 63, 426 (1989).ADSCrossRefGoogle Scholar
  35. 30.
    A. S. Davydov, Solitons in Molecular Systems (Reidel Publishing Co., Boston 1985).Google Scholar
  36. 31.
    Gerd Venzl and Signait F. Fischer, J. Chem. Phys. 81, 6090 (1984); Phys. Rev. B 32, 6437 (1985).ADSCrossRefGoogle Scholar
  37. 32.
    D. M. Alexander, Phys. Rev. Lett. 54, 138 (1985); D. M. Alexander and J. A. Krumhansl, Phys. Rev. B 33, 7172 (1986).ADSCrossRefGoogle Scholar
  38. 33.
    H.-B. Schüttler and T. Holstein, Ann. Phys. 166, 93 (1986).ADSCrossRefGoogle Scholar
  39. 34.
    A. C. Scott, Philos. Trans. R. Soc. London Ser. A 315, 423 (1985).ADSCrossRefGoogle Scholar
  40. 35.
    P. S. Lomdahl and W. C. Kerr, Phys. Rev. Lett. 55, 1235 (1985).ADSCrossRefGoogle Scholar
  41. 36.
    Albert F. Lawrence, James C. McDaniel, David B. Chang, Brian M. Pierce and Robert R. Birge, Phys. Rev. A 33, 1188(1986).ADSCrossRefGoogle Scholar
  42. 37.
    L. Cruzeiro, J. Haiding, P. L. Christiansen, O. Skovgaard, and A. C. Scott, Phys. Rev. A 37, 880 (1988).ADSCrossRefGoogle Scholar
  43. 38.
    Xidi Wang, David W. Brown, Katja Lindenberg, Phys. Rev. Lett. 62, 1796 (1989).ADSCrossRefGoogle Scholar
  44. 39.
    David W. Brown, Phys. Rev. B 39, 8122 (1989-II).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • David W. Brown
    • 1
  • Katja Lindenberg
    • 1
    • 2
  • Xidi Wang
    • 3
  1. 1.Institute for Nonlinear Science, R-002University of California at San DiegoLa JollaUSA
  2. 2.Department of Chemistry, B-040University of California at San DiegoLa JollaUSA
  3. 3.Department of Physics, B-019University of California at San DiegoLa JollaUSA

Personalised recommendations