Supercurrent decay in underdamped Josephson junctions: Nonstationary case

The decay of the zero voltage state in the presence of noise is investigated in connection with the general problem of a particle in a metastable state of a one-dimensional potential. A large number of important works have considered this problem on the basis of the analysis developed in the pioneering work by Kramers which stems from the condition of a thermal energy kT, small with respect to the potential barrier U0. This assumption legitimatizes the use of the stationary solutions of the Fokker--Planck equation. In the present work we developed an analysis in terms of the classical first-passage time problem due to Stratonovich whose results do not require the prescription kT<<U0. We confine attention to the case of very small damping which is of great interest in the context of Josephson junctions. Distributions of the switching currents are obtained which possess the correct normalization. Such a requirement cannot be satisfied by Kramers' results. Discrepancies between the two approaches and the influence of noise conditions and junction parameters are also discussed