Abstract

Co-author: Simone Zuccher (U. Verona)

Time evolution and interaction of filamentary structures is often studied by analysing dynamics in terms of local forces. An alternative route is to investigate physical or biological properties by focussing on geometric and topological properties of the surface swept out by filament motion. In this work we present new results on the evolution, interaction and decay of a Hopf link of quantum vortices governed by the Gross-Pitaevskii equation by analysing physical information in terms of the iso-phase Seifert surface swept out during the process [1]. We interpret the surface local twist as an axial flow acting along the vortex filament [2] and the Seifert surface of minimal area in terms of linear momentum of the system. We show that GP evolution is associated with a continuous minimisation of this surface in agreement with the physical cascade process observed. This approach sheds new light on filament dynamics and bears similarities to the study of fluid membranes in biological and chemical systems.

[1] Zuccher, S. & Ricca, R.L. (2017) Relaxation of twist helicity in the cascade process of linked quantum vortices. Phys. Rev. E 95 , 053109.
[2] Zuccher, S. & Ricca, R.L. (2017) Twist effects in quantum vortices and phase defects. Fluid Dyn. Res., doi.org/10.1088/1873-7005/aa8164.