Arrays of Josephson junctions in an environment with vanishing impedance

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunneling and charging e ffects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discu ssed with an emphasis on the inaccuracies in the Cooper pair Dumping. Renor malization of the Hamiltonian operator is used in order to reliably paramet rize the effects due to inhomogeneity in the array and nonideal gating sequ ences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.