Static and dynamic processes in a two-dimensional Josephson junction

A two-dimensional planar Josephson junction of an arbitrary cross section is considered. Electrodes are assumed to have a cross section identical with that of the junction. This configuration, which is correct from the physical point of view, allows the boundary conditions for the two-dimensional sine-Gordon equation to be determined uniquely through a distribution of a surface electrode current. The resulting problem, with this surface current distribution induced by the bias and/or external magnetic field, is trivial since it is a linear one. Square and rectangular cases are considered. The numerically derived results concerning the static and dynamic regimes differ significantly from the one-dimensional model because of a nonuniform transversal phase distribution. Moreover, a degeneration of static modes in the absence of an external magnetic field also appears. © 1996 The American Physical Society.