Exotic statistics of leapfrogging vortex rings

The leapfrogging motion of vortex 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 suggests that three-dimensional exotic exchange statistics is a common property of vortex rings in a variety of quantum liquids and gases. Potential applications range from helium superfluids to Bose-Einstein condensed alkali gases, metallic hydrogen in its liquid phases, and maybe even nuclear matter in extreme conditions.