Thermal fluctuations in moderately damped Josephson junctions: Multiple   escape and retrapping, switching- and return-current distributions and   hysteresis
  A crossover at a temperature T* in the temperature dependence of the width s of the distribution of switching currents of moderately damped Josephson junctions has been reported in a number of recent publications, with positive ds/dT and IV characteristics associated with underdamped behaviour for lower temperatures T<T*, and negative ds/dT and IV characteristics resembling overdamped behaviour for higher temperatures T>T*. We have investigated in detail the behaviour of Josephson junctions around the temperature T* by using Monte Carlo simulations including retrapping from the running state into the supercurrent state as given by the model of Ben-Jacob et al. We develop discussion of the important role of multiple escape and retrapping events in the moderate-damping regime, in particular considering the behaviour in the region close to T*. We show that the behaviour is more fully understood by considering two crossover temperatures, and that the shape of the distribution and s(T) around T*, as well as at lower T<T*, are largely determined by the shape of the conventional thermally activated switching distribution. We show that the characteristic temperatures T* are not unique for a particular Josephson junction, but have some dependence on the ramp rate of the applied bias current. We also consider hysteresis in moderately damped Josephson junctions and discuss the less commonly measured distribution of return currents for a decreasing current ramp. We find that some hysteresis should be expected to persist above T* and we highlight the importance, even well below T*, of accounting properly for thermal fluctuations when determining the damping parameter Q. 
J.C. Fenton and P.A. Warburton