Anomalous vortex diffusion in proximity-junction arrays

The classical motion of a single vortex in a proximity-junction array is investigated with the help of the effective-action formalism. The dynamics of the superconducting order parameter of each superconducting grain is assumed to be of the Langevin-type corresponding to local dissipation. The action describing the motion of the vortex in the array is shown to incorporate the propagator, the form of which in terms of the real-time dynamics corresponds to the logarithmical depression of mobility. Since in the array the motion of the vortex takes place in the effective periodic potential we check also that the presence of the periodic potential does not renormalize the anomalous behavior of the mobility in the low frequency limit. The results obtained are in agreement with experimental data on frequency dependence of the vortex contribution to proximity-junction-array response.