The Exotic Statistics of Leapfrogging Smoke Rings

TL;DR

This paper explores how the leapfrogging motion of smoke rings in three dimensions reveals exotic exchange statistics, suggesting such phenomena are common in various quantum fluids and gases.

Contribution

It demonstrates that three-dimensional exotic exchange statistics can be derived from hydrodynamical equations, extending the concept beyond two-dimensional systems.

Findings

Exotic exchange statistics can be computed using hydrodynamical Euler equations.

Leapfrogging smoke rings exhibit properties analogous to quantum exchange statistics.

Potential universality of these statistics across different quantum liquids and gases.

Abstract

The leapfrogging motion of smoke rings is a three dimensional version of the motion that in two dimensions leads to exotic exchange statistics. The statistical phase factor can be computed using the hydrodynamical Euler equation, which is a universal law for describing the properties of a large class of fluids. This suggests that three dimensional exotic exchange statistics is a common property of closed vortex loops in a variety of quantum liquids and gases, from helium superfluids to Bose-Einstein condensed alkali gases, metallic hydrogen in its liquid phases and maybe even nuclear matter in extreme conditions.