Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

Oleg Lychkovskiy

doi:10.1103/PhysRevA.91.040101

paper

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

arXiv:1403.7408 · doi:10.1103/PhysRevA.91.040101

Abstract

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 $v_{0}$ , and we are interested in its velocity at infinite time, $v_{\infty}$ . We derive a rigorous upper bound on $∣ v_{0} - v_{\infty} ∣$ for initial velocities smaller than the generalized critical velocity. In the limit of vanishing impurity-fluid coupling this bound amounts to $v_{\infty} = v_{0}$ 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 $v_{c L} = v_{s}$ (where $v_{c L}$ and $v_{s}$ are the Landau critical velocity and sound velocity, respectively) the latter regime is realized. For fluids with $v_{c L} < v_{s}$ 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.

arXiv commentv4: published version

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

Abstract

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