Critical velocity for vortex nucleation and roton emission in a generalized model for superfluids

We study numerically the process of vortex nucleation in the wake of a moving object in superfluids using a generalized and nonlocal Gross-Pitaevskii model. The nonlocal potential is set to reproduce the roton minimum present in the excitation spectrum of superfluid helium. By applying numerically a Newton-Raphson method we determine the bifurcation diagram for different types of nonlinearities and object sizes which allow for determining the corresponding critical velocities. In the case of a nonlocal potential, we observe that for small object sizes the critical velocity is simply determined by the Landau criterion for superfluidity, whereas for large objects there is little difference between all models studied. Finally, we study dynamically in two and three dimensions how rotons and vortices are excited in the nonlocal model of superfluid.