Vortex Nucleation Limited Mobility of Free Electron Bubbles in the Gross-Pitaevskii Model of a Superfluid

摘要

We study the motion of an electron bubble in the zero temperature limit whereneither phonons nor rotons provide a significant contribution to the dragexerted on an ion moving within the superfluid. By using the Gross-Clark model,in which a Gross-Pitaevskii equation for the superfluid wavefunction is coupledto a Schr\"{o}dinger equation for the electron wavefunction, we study howvortex nucleation affects the measured drift velocity of the ion. We useparameters that give realistic values of the ratio of the radius of the bubblewith respect to the healing length in superfluid $^4$He at a pressure of onebar. By performing fully 3D spatio-temporal simulations of the superfluidcoupled to an electron, that is modelled within an adiabatic approximation andmoving under the influence of an applied electric field, we are able to recoverthe key dynamics of the ion-vortex interactions that arise and the subsequention-vortex complexes that can form. Using the numerically computed driftvelocity of the ion as a function of the applied electric field, we determinethe vortex-nucleation limited mobility of the ion to recover values inreasonable agreement with measured data.