Induced vortex tunneling in a superconducting wire
  We consider induced topological transitions in a wire made from cylindrical superconducting film. During a transition, a pulse of electric current causes transport of a virtual vortex-antivortex pair around the cylinder. We consider both the instanton approach, in which the transition is viewed as motion of vortices in the Euclidean time, and the real-time dual formulation, in which vortices are described by a fundamental quantum field. The instanton approach is convenient to discuss effects of the environment, while in the dual formulation we show that there exists a potentially useful adiabatic regime, in which the probability to create a real vortex pair is exponentially suppressed, but the total transport of the vortex number can be of order one. 
S. Khlebnikov