Dr Michikazu Kobayashi (Kyoto University) gives a research seminar at the School of Mathematics, UEA. The talk is on “Energy and helicity cascades in non-Abelian quantum turbulence”. The abstract is below.

Quantum turbulence is realized as a dynamically and temporally complicated structure of quantized vortices in quantum fluid such as superfluid helium and atomic Bose-Einstein condensates. In this seminar, I talk about non-Abelian quantum turbulence comprised of non-Abelian quantized vortices, the topological charge of which is classified by the non-Abelian group. Being different from reconnecting dynamics of Abelian vortices, non-Abelian vortices show the formation of rung vortices when they collide keeping their linking topology. As a result, non-Abelian quantum turbulence shows a large-scale networking structure of vortices in which almost all vortices are connected. We also find several kinds of cascading processes in the wave-number space: inverse and direct cascades of the mass kinetic energy and helicity, respcetively, and direct cascade of the spin kinetic energy. I will show the expecting scenario connecting the dynamics of vortices and cascading processes. Our prediction can be tested in, for example, the cyclic phase of a spin-2 spinor Bose-Einstein condensate.

M. Kobayashi, et. al., Phys. Rev. Lett. 103 115301 (2009). M. Kobayashi and M. Ueda, arXiv:1606:07190.