Effect of thermal noise on the current-voltage characteristics of Josephson junctions

We analyze the influence of thermal noise on the Shapiro steps appearing in the current-voltage characteristics of Josephson junctions. We solve the Fokker-Planck equation describing the system by a path integral method in the steepest-descent approximation, previously applied to the stochastic resonance problem. We obtain the Asymptotic Time-Periodic Distribution P-as(phi, t), where phi epsilon [0, 2 pi] and compute from it the voltage [phi], constructing the I-V characteristics. We find a defined ''softening'' of the Shapiro steps as temperature increases, for values of the system parameters in the experimentally accessible range.