Is a doubly quantized vortex dynamically unstable in uniform superfluids?

TL;DR

This paper investigates whether doubly quantized vortices in uniform superfluids are dynamically unstable, showing through large-scale simulations that they remain unstable even in infinite systems, with instability linked to phonon radiation.

Contribution

The study demonstrates that doubly quantized vortices are inherently dynamically unstable in uniform superfluids, regardless of system size, using extensive Bogoliubov--de Gennes simulations and theoretical analysis.

Findings

Doubly quantized vortices remain unstable in the infinite system limit.

Splitting instability involves radiation of damped oscillatory phonons.

System-size dependence of excitation frequency was characterized.

Abstract

We revisit the fundamental problem of the 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, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.