Quasispin-operator description of the Josephson tunnel junction and the Josephson plasma frequency

This work deals with the description of the Josephson junction by means of quasispin operators. Several approximations of previous such treatments known as the pseudo-angular-momentum theory are dispensed with, and special care is taken to describe the charge imbalance across the junction in a physically proper way. The ensuing microscopic theory can be evaluated rigorously up to a very small error, yielding a closed system of dynamical equations for the macroscopic behavior of the junction which exhibit additional terms as compared to the usual Josephson relations. These terms leave the Josephson frequency practically unchanged, but are shown to yield a correction to the frequency of the Josephson plasma mode on the order of 1%.