We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting, the impurity is injected in the fluid with some initial velocity ${\mathbf{v}}_0$, and we are interested in its velocity at infinite time, ${\mathbf{v}}_{\infty }$. We derive a rigorous upper bound on $|{\mathbf{v}}_0-{\mathbf{v}}_{\infty }|$ for initial velocities smaller than the generalized critical velocity. In the limit of vanishing impurity-fluid coupling, this bound amounts to ${\mathbf{v}}_{\infty }={\mathbf{v}}_0$, which can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling, the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting, a small constant force is exerted upon the impurity. We argue that two distinct dynamical regimes exist—backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. For fluids with $v_{c\mathrm{L}}=v_s$ (where $v_{c\mathrm{L}}$ and $v_s$ are the Landau critical velocity and sound velocity, respectively), the latter regime is realized. For fluids with $v_{c\mathrm{L}}<v_s$, both regimes are possible. Which regime is realized in this case depends on the mass of the impurity, a nonequilibrium quantum phase transition occurring at some critical mass. Our results are equally valid in one, two, and three dimensions.

• Received 27 July 2014

DOI:https://doi.org/10.1103/PhysRevA.91.040101