Quantum dynamics of a fluxon in a long circular Josephson junction

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Abstract
The dynamics of the fluxon in a long circular Josephson junction is studied. A bias charge across the junction is shown to act like a gauge potential on the fluxon. The system is then quantized, and the energy levels of the fluxon are found to resemble those of a small capacity-dominated Josephson junction. The quantized fluxon is shown to exhibit a persistent motion in analogy with the persistent current of electrons in a metal ring threaded by a magnetic flux. This motion manifests itself in a voltage across the junction. At finite temperatures the voltage is reduced by the thermal distribution of the fluxon’s energy. The dependence of the voltage on the ratio of the junction’s circumference to the Josephson penetration depth is examined.