Dynamics of Quantized Vortices and Electron Bubbles in the Gross-Pitaevskii Model of a Superfluid

In this thesis we present an extensive study on quantised vortex dynamics using the Gross-Pitaevskii model of a superfluid in the limit of zero temperature. We make use of an accurate and robust numerical method that we developed to detect topological defects present in the scalar order parameter characterising the superfluid. We begin by focusing on the scattering of vortex rings by a superfluid line vortex. Thereafter, we focus on the development and decay of a turbulent vortex tangle, measuring the Vinen’s decay law for the total vortex length. Moreover, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade. The study of superfluid vortex reconnections is also carried out in order to identify what aspects of the reconnection process are universal. Aside from the investigation on quantised vortex dynamics, in this thesis we also present a study on the motion of an electron bubble in a superfluid. The electron bubble dynamics is studied in the adiabatic approximation using the Gross-Pitaevskii equation to model the superfluid wavefunction and a Schro¨dinger equation to model the electron wavefunction. This model allows us to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. We determine the vortex-nucleation limited mobility of the ion to recover values in reasonable agreement with measured data. Moreover, considering the scenario of an ion trapped on the core of a vortex line, we investigate how small and large amplitude Kelvin waves and solitary waves affect the drift velocity of the ion. In particular, we have identified that Hasimoto soliton-bubble complexes propagating along the vortex can arise