Overdamped soliton motion

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Abstract
The problem of finding the current carried by the driven, heavily damped, sine-Gordon chain has been solved by two methods. Trullinger et al. [Phys. Rev. Lett. 40, 206, 1603(E) (1978)] and Guyer and Miller [Phys. Rev. A 17, 1774 (1978)] have employed an approximate treatment of the hierarchy of equations generated by the Smolouchowski equation (the SEH method) to calculate the current analytically and numerically. Büttiker and Landauer [Phys. Rev. Lett. 43, 1453 (1979); and (unpublished)] have criticized this treatment and have proposed an alternate treatment employing ideas from nucleation theory (the NT method). These two methods of solution are reviewed and compared. Both methods are shown to involve the same ansatz for the nonequilibrium probability distribution function. The SEH method employs an exact integration of the steady-state one-particle current equation; the NT method employs an approximate integration of the steady-state nucleation current equation. The approximations underlying the use of the two methods are described. Criticism of the SEH method by Büttiker and Landauer is discussed.