Vortices in 2-D and 3-D superfluids

These lectures revolve around the interrelation between superfluidity and vortices. A superfluid system, such as helium, breaks gauge invariance by locally choosing a particular phase. Fluctuations in the phase give rise to the excitation spectrum of the system and to the topological excitations of the system, the quantized vortices. The equations of motion for the phase can describe situations in which the superfluid is accelerated, examples being first, second, third, and fourth sound. The phase can also change because of the motion of vortices, a topic known as phase slippage. In the first two lectures the idea of phase coherence is discussed, and how this idea leads very naturally to the description of phonon excitations, to second sound, and to the more exotic melting and freezing waves at the interface between solid and liquid helium; in the third and fourth lectures the topics are quantized vortices, their nucleation either by negative ions or by flow through orifices. In the last two lectures the ideas of vortex nucleation and phase slippage are applied to two-dimensional superfluids, that is to thin films of helium and to thin superconducting films. Here the vortices form bound pairs below a particular temperature corresponding to a phase transition. Phase slippage only occurs for unbound vortices, so the behavior is quite different above and below the transition temperature.