Pertubation analysis of the dynamical behavior of two-junction interferometers

The dynamical properties of symmetric quantum interferometers with equal junctions of negligible capacitance have been studied by means of perturbation analysis in the limit of small values of the parameter β. In this limit, two characteristic time constants arise. These quantities may be linked to two different dynamical processes in the system: the first is related to the time evolution of the average superconducting phase difference across the two junctions; the second defines the time scale for flux motion. The response of the system to constant and time-dependent externally applied magnetic fields is considered and a general perturbed solution for the average superconducting phase difference and the fluxon number variable is derived to first order in β.