Aspects of thermal activation theory and applications to the Josephson effect

The problem of the thermal induced escape of a Brownian particle from a metastable state is studied in the overdamped limit by the first-passage time technique. It provides an extension of Kramers’ results to the case of an energy barrier U0 close to the thermal energy kT. Differences between this approach and that of Kramers for low barrier energy are quantified in the specific example of a Josephson junction. In the case of periodic potential and stationary conditions, our calculations reproduce the results by Ambegaokar and Halperin. This approach can also be applied to the case of an rf SQUID.