Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid.
Oleg Lychkovskiy, Russian Quantum Center, Moscow
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 (which is below the critical velocity), and we enquire about its velocity at inﬁnite time, v_inf. We derive a rigorous upper bound on |v_0 − v_inf|. In the limit of vanishing impurity-ﬂuid coupling, this bound amounts to v_inf = v_0, which is anticipated from the Landau criterion of superﬂuidity. In the case of a ﬁnite coupling, the velocity of the impurity can decrease, but not to zero; the bound quantiﬁes the maximal possible decrease.
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. Which regime is realized depends on the mass of the impurity. A nonequilibrium quantum phase transition occurs at some critical mass.