Two Critical velocities for a superfluid in a periodic potential

In contrast to a homogeneous superfluid which has only one critical velocity, there exist two critical velocities for a superfluid in a periodic potential. The first one, which we call inside critical velocity, is for a macroscopic impurity to move frictionlessly in the periodic superfluid system; the second, which is called trawler critical velocity, is the largest velocity of the lattice for the superfluidity to maintain. The result is relevant to the superfluidity observed in the Bose-Einstein condensate in an optical lattice and supersolid helium.