Advertisement

Classical Statistical Mechanics of Soliton-Bearing Systems

  • T. Schneider
  • E. Stoll
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 23)

Abstract

We review the status of classical statistical mechanics for some 1-D soliton or solitary wave-bearing systems. Much of the recent activity is attributable to the motivating impact of molecular-dynamics (MD) results on discrete Φ4-[1–4] and sine-Gordon (sG) systems [5, 6] and the Toda lattice [7], which revealed the need for including soliton features in a statistical description, in particular, of dynamic properties. In keeping with these model systems, we discuss the evidence for kink, breather (envelope-soliton) and pulse-soli ton effects, including the associated new excitation branches. Primary attention is given to: a) thermodynamic properties and static form factors, and b) dynamic form factors (DFF) and displacement patterns.

Keywords

Toda Lattice Toda Chain Classical Statistical Mechanic Pulse Soliton Breather Solution 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Schneider, E. Stoll: Phys. Rev. Lett. 31, 1254 (1973)CrossRefADSGoogle Scholar
  2. 2.
    T. Schneider, E. Stoll: Phys. Rev. Lett. 35, 296 (1975)CrossRefADSGoogle Scholar
  3. 3.
    S. Aubry: J. Chem. Phys. 64, 3392 (1976)CrossRefADSGoogle Scholar
  4. 4.
    T.R. Koehler, A.R. Bishop, J.A. Krumhansl, J.R. Schrieffer: Solid State Commun. 17, 1515 (1975)CrossRefADSGoogle Scholar
  5. 5.
    T. Schneider, E. Stoll: Phys. Rev. Lett. 41, 1429 (1978)CrossRefADSGoogle Scholar
  6. 6.
    E. Stoll, T. Schneider, A.R. Bishop: Phys. Rev. Lett. 42, 937 (1979)CrossRefADSGoogle Scholar
  7. 7.
    T. Schneider, E. Stoll: To be publishedGoogle Scholar
  8. 8.
    R.K. Bullough, R.K. Dodd: “Solitons in Mathematics: Brief History”, in Solitons and Condensed Matter Physios, ed. by A.R. Bishop, T. Schneider, Springer Series in Solid-State Sciences, Vol. 8 (Springer, Berlin, Heidelberg, New York 1978) p.2Google Scholar
  9. 9.
    M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur: Phys. Rev. Lett. 30, 1262 (1973)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    M. Toda: J. Phys. Soc. Japan 22, 431 (1967)CrossRefADSGoogle Scholar
  11. 11.
    U.M. Toda: Prog. Theor. Phys. Suppl. 45, 174 (1970)CrossRefADSGoogle Scholar
  12. 12.
    T. Schneider, E. Stoll: To be publishedGoogle Scholar
  13. 13.
    J.F. Currie, J.A. Krumhansl, A.R. Bishop, S.E. Trullinger: To be publishedGoogle Scholar
  14. 14.
    A.R. Bishop: To be publishedGoogle Scholar
  15. 15.
    A.R. Bishop: Solid State Commun. 30, 37 (1979)CrossRefADSGoogle Scholar
  16. 16.
    K. Kawasaki, Prog. Theor. Phys. 55, 2029 (1976)Google Scholar
  17. 17.
    G.F. Mazenko, P.S. Sahni: Phys. Rev. B 18, 6139 (1978)CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    T. Schneider, E. Stoll: To be publishedGoogle Scholar
  19. 19.
    J.M. Loveluck, T. Schneider, E. Stoll, H.R. Jauslin: “A Comparison of Static and Dynamic Properties of One-Dimensional Magnets and Corresponding sG Systems”, in this volume, p.157Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • T. Schneider
    • 1
  • E. Stoll
    • 1
  1. 1.IBM Zurich Research LaboratoryRüschlikonSwitzerland

Personalised recommendations