Topological invariance of superconducting arrays

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Abstract
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.