Stochastic Langevin coefficients associated with the drift and diffusion coefficients shown in Fig. 11. Left panel: illustration of the Langevin drift coefficient L_t → h(L_t,I_t). Following Eq. (64), this coefficient gives the mean direction of motion for a given location in action space. Right panel: illustration of the Langevin diffusion coefficient L_t → g(L_t,I_t). This coefficient describes the jitter of wires around the mean flow given by h. In particular, it allows wires to stochastically penetrate the barrier.