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 $j<{j}_{t}$ to the motion of the vortex crystal at $j>{j}_{t}$. 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.