Dynamic Melting of the Vortex Lattice

We investigate analytically and numerically the melting of the vortex lattice moving in an inhomogeneous environment under the applied current $j$. We predict the existence of a dynamic phase transition at some characteristic current $j=j_t$ (crystallization current) from the motion of the amorphous vortex configuration at $j<\mathrm{}{j}_t$ to the motion of the vortex crystal at $j>\mathrm{}{j}_t$. The crystallization current $j_t$ exceeds essentially the critical current $j_c$ for strongly disordered systems and diverges as temperature approaches the melting temperature $T_m$ of the undisturbed lattice.