Current-voltage characteristic of a Josephson junction with randomly distributed Abrikosov vortices

We have developed a theory of the current-voltage characteristic of a Josephson junction in the presence of randomly distributed, pinned misaligned Abrikosov vortices oriented perpendicularly to the junction plane. Under these conditions the Josephson phase difference $\phi$ acquires an interesting stochastic dependence on the position in the plane of the junction. In this situation it is possible to define an average critical current which is determined by the spatial correlations of this function. Due to the inhomogeneity, we find that for finite voltage bias the electromagnetic waves propagating in the junction display a broad spectrum of wavelengths. This is at variance with the situation encountered in homogeneous junctions. The amplitude of these modes is found to decrease as the bias is increased. We predict that the presence of these excitations is directly related to a remarkable feature in the current-voltage characteristic. The dependence of the position and the magnitude of this feature on the vortex concentration has been determined.