Brownian Motion of Coupled Nonlinear Oscillators: Thermalized Solitons and Nonlinear Response to External Forces

Abstract

We study the steady-state dynamical behavior of a set of torsion-coupled pendula in the presence of damping, fluctuating thermal torques, and constant applied torque. For small applied torque, the average angular velocity of the pendula at low temperature is associated with the motion of thermalized sine-Gordon solitons and as the torque is increased the velocity response becomes strongly nonlinear. These results can be used to describe nonlinear response in Josephson transmission lines and weakly pinned one-dimentional charge-density-wave condensates.