Dynamics of an RF-driven Josephson junction near the bifurcation point

We investigate the dynamics of an RF driven Josephson junction coupled to thermal heath bath. We present a stochastic semiclassical equation of motion for the junction, obtained from a microscopic Hamiltonian of the system. We discuss conditions when the Langevin forces in this equation can be approximated by Markovian white noise. For this case, we obtain the Fokker-Planck equation, which we numerically solve to describe the switching process between two stable states near the bifurcation point.