Metastable transition times of the 1D dynamical sine-Gordon model

We study the dynamics of a stochastic heat equation with $\gamma\sin(\beta u)$ nonlinearity on one-dimensional torus. We show an Eyring--Kramers law for the jump rate between potential wells in the small-noise limit, and that the transition state undergoes a bifurcation at $\gamma\beta = 1$. The argument follows the potential-theoretic approach of Berglund and Gentz [Electron. J. Probab. 2013].