Abstract
Motion of a driven and heavily damped sine-Gordon chain with a low density of kinks and tight coupling between particles is controlled by the nucleation and subsequent annihilation of pairs of kinks and antikinks. We show that in the steady state there are no spatial correlations between kinks or between kinks and antikinks. For a given number of kinks and antikinks all geometrical distributions are equally alike, as in equilibrium. A master equation for the probability distribution for the number of kinks on a finite chain is solved, and substantiates the physical reasoning in previous work. The probability distribution characterizing the spread along the direction of particle motion of a finite chain in equilibrium as well as in the driven overdamped case is derived by simple combinatorial considerations. The spatial spread of a driven chain in the thermodynamic limit does not approach a steady state; a given particle followed in time deviates as t1/2 from its average forced motion. This result follows from the hydrodynamic equations for the dilute kink gas. Comparison is made with other recent results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. E. Trullinger, M. D. Miller, R. A. Guyer, A. R. Bishop, F. Palmer, and J. A. Krumhansl,Phys. Rev. Lett. 40:206, 1603 (1978).
M. Büttiker and R. Landauer,Phys. Rev. Lett. 43:1453 (1979).
K. E. Lonngren and A. Scott, eds.,Solitons in Action (Academic, New York, 1978).
A. R. Bishop and T. Schneider, eds.Solitons and Condensed Matter Physics (Springer, Heidelberg, 1978).
R. D. Parmentier, inSolitons in Action, K. E. Lonngren and A. Scott, eds. (Academic, New York, 1978), p. 173.
P. M. Marcus and Y. Imry,Solid State Commun. 33:345 (1980).
R. Landauer, inThe Maximum Entropy Formalism, R. D. Levine and M. Tribus, eds. (MIT Press, Cambridge, Mass., 1978), p. 321; see Appendix.
A. Seeger and P. Schiller, inPhysical Acoustics, Vol. III, W. P. Mason, ed. (Academic, New York, 1966), p. 361.
J. Rubinstein,J. Math. Phys. 11:258 (1970).
F. C. Frank,J. Cryst. Growth 22:233 (1974).
J. I. Lauritzen Jr.,J. Appl. Phys. 44:4353 (1973).
J. Keizer,J. Stat. Phys. 6:67, 1972.
R. E. Burgess,Physica 20:1007 (1954);Proc. Phys. Soc. (London) B69:1020 (1956).
J. E. Hill and K. M. van Vliet,J. Appl. Phys. 29:177 (1978).
A. D. Brailsford,Phys. Rev. 122:778 (1961);128:1033 (1962);137A:1562 (1965).
W. van Roosbroeck,Phys. Rev. 91:282 (1953).
S. O. Rice, inSelected Papers on Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954), p. 133.
H. Thomas, inNoise in Physical Systems, D. Wolf, ed. (Springer, Heidelberg, 1978), p. 278.
J. A. Krumhansl and J. R. Schrieffer,Phys. Rev. B 11:3535 (1975).
C. M. Varma,Phys. Rev. B 14:244 (1976).
M. A. Collins, A. Blumen, J. F. Currie, and J. Ross,Phys. Rev. B 19:3630 (1979).
T. Schneider and E. Stoll,Phys. Rev. Lett. 41:1429 (1978).
Y. Imry and B. Gavish,J. Chem. Phys. 61:1554 (1974).
L. Gunther and Y. Imry,Phys. Rev. Lett. 44:1225 (1980).
L. Gunther and D. L. Weaver,Phys. Rev. B 20:3515 (1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bennett, C.H., Büttiker, M., Landauer, R. et al. Kinematics of the forced and overdamped sine-Gordon soliton gas. J Stat Phys 24, 419–442 (1981). https://doi.org/10.1007/BF01012814
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01012814