RIGOROUS ANALYTICAL RESULTS ON PHASE-LOCKING IN JOSEPHSON-JUNCTION LADDER ARRAYS

Based on a previously developed analytical procedure combining ideas f rom the first harmonic approximation with those from the slowly varyin g phase we obtain some rigorous analytical results on the dynamics of two-dimensional Josephson-junction ladder arrays composed of an arbitr ary number of cells. We are able to derive a general analytic expressi on for the reduced equations governing phase locking of the cells. Whi le solving these reduced equations seems not to be possible in general , we were able to evaluate them up to the end for three experimentally relevant cases: (i) arrays composed of strongly damped junctions and small ring inductances without an external shunt, (ii) arrays composed of strongly damped junctions and small ring inductances with an exter nal shunt, and (iii) arrays composed of strongly damped junctions and large ring inductances without an external shunt.