Numerical study of induced vortex tunneling
  Tunneling of vortex-antivortex pairs across a superconducting film can be controlled via inductive coupling of the film to an external circuit. We study this process numerically in a toroidal film (periodic boundary conditions in both directions) by using the dual description of vortices, in which they are represented by a fundamental quantum field. We compare the results to those obtained in the instanton approach. 
C. D. Bass and S. Khlebnikov