Interference and transmission of quantum fluxons through a Josephson ring

The influence of quantum interference on the transmission of a fluxon through an ideal long circular Josephson junction (a "Josephson ring") is studied. In the low-temperature regime the transmission is a periodic function of a gauge charge applied along the ring with a period 2e. Around points of full period of both the gauge charge and the optical path, the transmission shows resonances as a function of the gauge charge and "antiresonances" as a function of the optical path. These resonances and antiresonances are associated with energy levels of the circular junction and with short dwelling time of the fluxon in the ring. In the high-temperature regime the interaction with plasmons dephases the fluxon wave function completely. The transmission probability in this regime is calculated in a stationary picture and in a dynamical picture and two different results are obtained. The discrepancy between the two pictures is explained via the ratio of the dwelling time to the time the thermal bath needs to change the plasmons' microscopical state. A general method that retrieves the two results is presented.