On quantum vortex reconnections

The thesis analyzes the phenomenon of quantum reconnections in superfluids, in particular in Bose–Einstein condensates, governed by the Gross–Pitaevskii Equation (GPE). The investigation is applied to two distinct settings. First we study the reconnection between an inclined vortex ring and a straight vortex line, where the vortex ring inclination angle is varied. We analyze the evolution throughout the dynamics of the total length and curvature of the vortex filaments for different values of the inclination angle, as well as the redistribution of total energy among its components during the reconnection process. By applying the Helmholtz decomposition of the kinetic energy, we further characterize how the inclination angle affects the partition between incompressible and compressible components, highlighting the respective roles of Kelvin wave generation and sound emission. The results of the energy analysis are then compared with the evolution of the vortex line length and the curvature, in order to identify possible correlations between the inclination angle, geometric features, and energy redistribution during reconnection. Then we study the vortex reconnection between two perpendicular straight vortex lines in immiscible two-component BECs. The vortices are located in the majority component, whereas their cores are filled by the minority component. By systematically varying the number of atoms in the second condensate, we investigate how the minority component affects the reconnection dynamics. Hence we analyze the parameters of the scaling law in order to assess whether the reconnection process remains unchanged or becomes faster or slower.