We study in an analytical way the response of a Josephson-junction array to an alternating applied current. From the dynamic equation governing the time evolution of the system, an effective Hamiltonian describing the low-temperature stationary state is obtained. The quantized voltage steps are then shown to result from topological invariance of the system. The relevance of boundary conditions and ground-state degeneracies is also discussed.

• Received 1 May 1992

DOI:https://doi.org/10.1103/PhysRevB.46.564