Elementary excitations and quantized vortices in bosonic superfluids

In this work we studied two sistems of bosonic superfluids at zero temperature, ultra-cold Bose gases and superfluid helium, within a simple classical field formalism and we underlined differences and similarities between them. We also analyzed how the presence of strong interactions, as in the case of helium, modifies the quasiparticle excitation spectrum and subsequently the vortex line density profile. After a general review about these bosonic systems properties we started in general from the Hartree equation of a bosonic system and, with different hypotesis on the interaction potential between bosons, we obtained the equations describing the two above mentioned systems, mainly focusing on elementary quasiparticle excitations and quantized vortices. Furthermore throughout this work the results were compared with experimental data and aftermaths of the main theories in literature.