Nucleation of the phase of a finite Josephson junction

We present the results of a study of thermal and quantum nucleation in an overlap Josephson junction with a finite length. There is a critical length that marks the boundary between nucleation with a uniform phase across the junction and nucleation that is concentrated at one of the ends of the junction. In the thermal activation regime, it is shown to be , while at absolute zero, in the quantum tunnelling regime, it is given by . Here, is the effective Josephson penetration depth. The rates for nucleation at the ends of the junction are given for junctions in the thermal activation regime for all lengths, and for junctions undergoing quantum nucleation at absolute zero temperature for lengths less than or equal to the critical length.