# Vortex Phases

Quantum vortices are topological excitations in many-body quantum fluids that carry angular momentum and interact over large distances due to their long-range velocity fields. In planar confinement quantum vortices bound in a container can exhibit rich and surprising behavior, first noticed by Onsager in his 1953 pioneering study.

Onsager noticed the significance of a key property of planar quantum vortices: they have reduced degrees of freedom. Unlike classical particles, quantum vortices do not have both position and momentum. Instead the x position is conjugate to the y position (which acts as a x momentum!). This observation led to the concept of negative temperature: a bounded phase space sets strict limits on the way a system can increase its entropy as it absorbs energy. In fact, the entropy has a maximum, and beyond this point, the absolute Boltzmann temperature becomes negative! Physically, above a critical point, the vortices can only absorb energy by clustering together, creating high energy quantum storms.

We have explored these ideas in the context of dilute gas Bose-Einstein condensates, a compressible quantum fluid. One key question is that of the role of dissipation. While BECs are very cold, they are not entirely immune to dissipation. Although it would be reasonable to expect high energy vortex clusters to be very fragile and prone to mutual annihilation with anti-clusters, we proposed an experiment to create large clusters, in which they were found to be very long-lived. This longevity arises from the strong polarization of high energy clustered systems - there is no chance for vortices to annihilate if they are in large separated clusters and hence unable to encounter antivortices. Once clusters form, they can retain their energy due to large scale polarization.

Selected publications on vortex statistical mechanics are below.