Synchronization in networks of superconducting wires

We study the synchronization phenomena in networks of superconducting wires driven by quenched random external currents. Each wire interacts with all the other wires perpendicular to it; this system naturally presents an example of the well-known phase model. The equations of motion are obtained from current conservation conditions, which in turn lead to an effective Hamiltonian of the system. We then use the replica method to derive the self-consistency equations and obtain the phase diagram. Effects of alternating currents as well as the possibility of glassy behavior are also discussed. copyright 1997 The American Physical Society