Charging corrections to the Josephson Hamiltonian

Starting from a microscopic model which includes a charging term, we derive an effective, single-degree-of-freedom Hamiltonian, describing a Josephson junction. We obtain corrections to the standard Josephson Hamiltonian, which hybridize coordinate and momentum operators. The resulting equation of motion is analyzed in the classical limit, and the corresponding I-V characteristics are obtained. We predict that, in a certain range of the parameters, the branching point in the I-V curve and the effective resistance of the junction exhibit reentrant behavior as a function of both the self-capacitance and the normal resistance of the junction.