Superfluidity of disordered Bose systems: numerical analysis of the Gross-Pitaevskii equation with random potential

We study the two-dimensional superfluidity of disordered Bose systems by analyzing the Gross-Pitaevskii equation with random potential. First, we obtain the ground state and calculate its superfluid density by the linear response theory. The superfluid density shows their remarkable dependence on the potential amplitude, the healing length and the density. Secondly, we apply the velocity field to the ground state to observe the breaking of superfluidity due to the excitation of vortex pairs above a critical velocity