Models for supercritical motion in a superfluid Fermi liquid.

We study objects moving in a Fermi superfluid at velocities on the order of the Landau velocity $v_L$. We introduce a boundary condition that describes diffuse reflection of quasiparticles on a scale larger than the coherence length. Applying this boundary condition we calculate the drag force on steadily moving objects of different sizes. For a point-like particle we find a critical velocity at $v_L$. For a macroscopic cylinder we need to take into account the spatially varying flow field. At low velocities this arises from ideal flow of the superfluid. At higher velocities the flow field is modified by excitations that are created when the flow velocity locally exceeds $v_L$. We investigate multiple limiting cases. In the absence of quasiparticle-quasiparticle collisions we find a critical velocity slightly higher than $v_L$, and the drag force at $2v_L$ is reduced by an order of magnitude compared to the point-like particle. In a collision-dominated limit the flow shows signs of instability at a velocity below $v_L$.