Vortex crystals with empty and filled cores

A generic quasi 2 dimensional superfluid confined in a rotating circular trap could present quantum vortices. According to the Point Vortex model, vortex is effectively described as a point-like particle around which the superfluid flows with quantized circulation. It has been proven that at equilibrium the vortex-array is a composition of concentric regular polygonal structures. Non-trivial excitations of these stable configurations are the so called Tkachenko modes, microscopically associated to elliptical precessions of each vortex around its equilibrium position, representing a macroscopic deformation of the vortex-crystal. Recently it has been also proposed a model for point-like vortices hosting in their cores massive particles. The goal of this thesis is the characterization of the main effects ensuing from the “vortex mass” on the formation of the vortex-crystal depending on the rotation rate of the trap and on the creation of their non-trivial excitations. Principal consequences of such a massive description are the centrifugal forces acting on each massive vortex core and the typical cyclotronic-like orbits characterizing their dynamics. The study was carried out in an analytical way, and was based on the minimization of system's free energy,as well as on the study of the equations of motions of many-vortex systems.