Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid

Abstract

We study the motion of an electron bubble in the zero-temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the GrossClark model, in which a Gross-Pitaevskii equation for the superfluid wave function is coupled to a Schrödinger equation for the electron wave function, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid 4 He at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex nucleation limited mobility of the ion to recover values in good agreement with measured data.

Density functional theory modeling of vortex shedding in superfluid He4

“…5, has also been observed experimentally for the electron bubble. 10,21 Lastly, our simulations show that the critical velocity decreases as a function of the object size as demonstrated in Fig. 5 (see also Fig.…”

“…8 By coincidence, this value closely matches the critical velocity for vortex ring emission for the electron bubble at zero pressure. 1,10,43,44 However, much lower values (down to few cm/s) are typically seen at larger length scales, 8 which clearly shows that v L must scale with the object size, as was also shown by recent numerical simulations of a moving wire in superfluid 4 He in 2-D geometry. 46 Comparison of our OT-DFT calculations with the previous GP results shows that the same vortex ring emission process can take place in both models, which clearly demonstrates that rotons do not play a major role in the onset of dissipation nor in the existence of the critical velocity.…”

“…The Gross-Pitaevskii model, despite its shortcomings, is often applied to model superfluid helium. 10,51,52 As GP is known to model only the phonon branch of superfluid helium dispersion relation, it is typically employed with parametrization that matches the speed of sound (GP Model 1 in Fig. 2).…”

“…[9][10][11][12][13][14][15][16]49,50 Although the GP equation is a rather poor model for superfluid helium, it has been shown to reproduce the vortex ring emission dynamics for an electron moving in the liquid at 0 K as well as the inherent symmetry breaking of the solution due to the emerging instability (see Ref. 10 and references therein). It is well-known, however, that GP theory can at most reproduce the phonon part of the superfluid helium dispersion relation and, consequently, it cannot provide accurate description of the vortex core structure.…”

Interaction between active particles and quantum vortices leading to Kelvin wave generation

“…The GP equation governs the dynamics of the macroscopic wave function of the system, hence quantum vortices are naturally included. In the GP framework, impurities and particles are often described in terms of classical fields [20][21][22][23]. In particular, it was shown by Roberts and Rica [22] that, depending on the coupling constants, the impurity field separates from the condensate and the two fields become immiscible.…”