Anomalous vortex dynamics in two-dimensional superconducting arrays

The dynamical response of a superconducting array, modeled by the two-dimensional classical XY model, is studied by using equations of motion for vortices and spin waves. The vortex conductivity σᵥ is evaluated in the framework of Mori's formalism. σᵥ has a finite zero-frequency limit in the case of a spin dynamics corresponding to the resistively shunted junction model, but it goes to zero logarithmically with frequency for a Landau-Ginzburg dynamics. The latter behavior has been observed in recent experiments and computer simulations.