Finite-damping corrections to the conductivity of the sine-Gordon chain: General formalism and asymptotic results

We develop a systematic method for obtaining finite-damping corrections to the Smoluchowski equation describing the Brownian motion of coupled nonlinear oscillators. The formalism is applied to the driven sine-Gordon pendulum chain to obtain the lowest-order correction to the conductivity theory by Trullinger et al., and asymptotic results are presented in the limits of (i) low-torque, low-temperature, strong coupling, (ii) high-torque, all temperatures and coupling strengths, and (iii) vanishing coupling between pendula.