MIT

Title: Do vortices have mass ?

Abstract: My small daughter doesn't always like it when bathtime ends, but even she can tell that vortices are noticeable features in fluids, standing out from the background ripples and flows around them. They comprise a few salient degrees of freedom emerging from a vast number of less interesting ones, and so vortices are good poster children for physicists' general campaign to describe the salient features of the universe with simple models. The dynamics of vortex collective co-ordinates has peculiar features, such as the Magnus effect and long range interactions. Controversy has endured, however, over whether vortex dynamics has the ordinary feature of a Newtonian mass. This old issue has basic implications for such current questions as the emergence of quantum effects in rapidly rotating Bose-Einstein condensates, and the nature of vortex-particle duality. And in these modern fluid systems it can be directly and rigorously investigated, both theoretically and experimentally.

I will describe my recent theoretical work with David Thouless, explaining our rigorous results on vortex masses (or their absence) in several different fluid dynamical systems, including BEC. I will gloss over most of the Bessel functions, after indicating how they basically go together, to present our results and emphasize the principles that we learn from the various models. There will be some cautionary notes about neglecting short distance physics that may be worth remembering for cold atom physics in general.