Splitting instability of a doubly quantized vortex in homogeneous superfluids

We revisit the fundamental problem of splitting instability of a doubly-quantized
vortex in uniform single-component superfluids at zero temperature. We analyze
the system-size dependence of the excitation frequency of a doubly-quantized
vortex through large-scale simulations of the Bogoliubov–de Gennes equation,
finding that the system remains dynamically unstable even in the
infinite-system-size limit. The perturbation and semi-classical analyses reveal
that the splitting instability radiates a damped oscillatory phonon as a
counterpart of a quasi-normal mode.