Abstract
Unlike Bose-Einstein condensation, which occurs in a perfect gas, superfluidity is a phenomenon that requires interactions between particles. Indeed, one of the criteria for superfluidity - the existence of permanent currents - is not satisfied in an ideal gas: it is the repulsive interactions between particles that ensure that a current can exist in a metastable state, protected by an energy barrier from relaxation to the ground state.
The aim of this third lecture was to explore in detail the essential role of interactions. We began with a qualitative description of their impact in terms of fragmentation, hybridization and entanglement of the quantum state of the fluid. We then studied the Gross-Pitaevskii energy functional and the associated Bogoliubov formalism. This enabled us to quantitatively determine the energy spectrum of the interacting gas. We established the Landau criterion, which expresses the condition under which a superfluid flow can be stable with respect to a perturbation. We also examined how to go beyond this criterion by studying the braking of a superfluid flow by nucleating pairs of quantum vortices.
