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Networks of Josephson junctions and their synchronization

One can demonstrate that a 1-D Josephson network containing junctions with different resistances can be synchronized at frequencies, which are multiples of 2eV, where V is the total d.c. voltage applied across the network. The appearance of such synchronization follows from the law of charge conservation and takes place if charge transfer is dominated by the Josephson channel. One can observe also a sub-harmonic structure. The result holds for cluster-based arrays as well as for general case of a tunneling network.