Charge representation of a small two-dimensional Josephson-junction array in the quantum regime

Using the charge representation, we calculate the ground state energy and the critical current of a small two-dimensional Josephson junction array subject to both charge and magnetic frustration. In the quantum regime the ground state of the array is a superposition of charge states, allowing a supercurrent to flow through the circuit. Both the ground state energy and the critical current can be tuned by the two frustrations. We show that the notion of a vortex is compatible with a charge representation of the array. {copyright} {ital 1996 The American Physical Society.}