Quantum coherence and duality in Josephson junctions

The contribution to the partition function of the instanton tunneling between degenerate vacua is investigated for systems of Josephson junctions with gauge charge induced by external sources. Effects of weak dissipation both due to quasiparticle tunneling and due to shunt resistance are considered via a perturbative method for one- and two-junction cases. The tunneling partition functions display oscillating behavior as functions of the gauge charge, generating oscillating voltages in the presence of external currents. The duality relation in the system is also discussed: In particular, the strong-coupling limit and the weak-coupling limit of a ring of N junctions map onto each other.