Josephson Vortex Bloch Oscillations: Single Pair Tunneling Effect
  We consider the Josephson vortex motion in a long one--dimensional Josephson junction in a thin film. We show that this Josephson vortex is similar to a mesoscopic capacitor. We demonstrate that a single Cooper pair tunneling results in nonlinear Bloch--type oscillations of a Josephson vortex in a current-biased Josephson junction. We find the frequency and the amplitude of this motion. 
R.G. Mints and I.B. Snapiro