Boson Mapping and Nonlinear Response of Type-II Superconductors
  The vortices in a high-Tc superconductor with strong correlated pinning centers have been studied numerically using the mapping to charged bosons in two-dimensions(2D) and the Monte-Carlo algorithm. Considering the viscous dissipation of moving vortices we derived a nonlinear voltage response expression which describes different regimes and their crossover uniformly. This equation accords with experimental results. 
H.D.Chen, W.P.Bai, D.L.Yin, Y.L.Zhu, G.Li and C.Y.Li