Topological Hall Angles and Lifetime Hierarchies of Knotted Vortex Filaments

Recent measurements of mutual friction in strongly interacting Fermi superfluids establish a direct link between the transverse dynamics of quantized vortices and the relaxation of localized core states. Motivated by these results, we investigate the dynamics of knotted vortex filaments within an effective hydrodynamic framework. By extending the vortex Hall angle formalism to non-planar filament geometries, we derive a phenomenologically motivated scaling relation between filament topology and internal relaxation times. We show that a hierarchy of decay times emerges naturally from a topology-dependent Reynolds-like barrier, with lifetimes controlled by writhe-dependent geometric phase lags. While no claim is made of microscopic particle identity, the resulting hierarchy closely parallels the ordering observed in several physical systems exhibiting metastable topological excitations.