Self-trapped electrons in liquid helium II

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

“…Consequently, the ion moves of -center with respect to the axis of the nucleated ring and is thus recaptured. We note that for these low electric fields, the nucleation always takes place at the critical velocity v c ∼ 0.32 [15]. Such a value of the critical velocity can be explained in terms of the motion of a sphere in an incompressible fluid as discussed by Berloff et al [15] and Frisch et al [40].…”

“…We note that for these low electric fields, the nucleation always takes place at the critical velocity v c ∼ 0.32 [15]. Such a value of the critical velocity can be explained in terms of the motion of a sphere in an incompressible fluid as discussed by Berloff et al [15] and Frisch et al [40]. By working within a potential flow approximation of a classical fluid, it is known that the flow around such an object has a maximum velocity at the equator equal to 3/2U ∞ , where U ∞ is the velocity in the far field.…”

“…We begin by adopting the Gross-Clark model [14,15] in which superfluid 4 He is modeled by a GP equation. The energy of the system is then given by the Hamiltonian…”

“…We note that such a model does not provide an accurate description for 4 He since it neither reproduces the correct equation of state nor does it describe the correct dispersion relation since a roton minimum is not present. However, it has been shown by Berloff and Roberts [15] that this model can account for the deformations affecting the bubble in its motion and it also captures all the main qualitative physics characterizing the interaction between electron bubbles and superfluid vortices. We note that it has recently been shown that a vortex filament description of a superfluid can be systematically derived from the GP equation [16].…”

“…Since there is no universally accepted microscopic model for liquid helium, we will adopt the so-called Gross-Clark model [14,15] to study the three-dimensional (3D) motion of an electron bubble within a superfluid. In this model, a Schrödinger equation describing the wave function of the electron is coupled to a mean-field equation of a superfluid.…”