Nucleation of Weakly Driven Kinks

We study nucleation of kink-antikink pairs under weak nonequilibrium conditions and in the strong friction limit. We introduce an effective critical nucleus of size $s_0$, which is small compared to the inverse kink density but large compared to a kink size. We evaluate independently the nucleation rate and the kink lifetime from a multidimensional Kramers theory and by studying kink-antikink annihilation processes. We find a kink density which is independent of $s_0$ and of the driving force in this regime. The result is in accordance with the equilibrium kink density obtained from statistical mechanics.