Abstract
In this lecture, our aim has been to go beyond the purely phononic model for gas excitations and take vortices into account. Their influence can be understood intuitively: suppose we have - after taking phonons into account - a certain phase coherence between two points A and B; if a vortex with its phase winding of 2π can be randomly inserted on segment AB, the phase difference will flip between its initial value and this value plus π. This random phase shift will result in the loss of all coherence between A and B, and the quasi-phase order that may have existed between these two points will be destroyed. We first studied the role of an isolated vortex, then of a pair of vortexes with opposite circulations, before turning to the thermodynamics of a vortex assembly. Finally, we addressed the role of vortices in the renormalization group. This enabled us to establish a clear criterion for superfluidity; in particular, we found that the superfluid density in phase space is either zero or greater than 4.
