# Breather induced quantized superfluid vortex filaments and their characterization

## TL;DR

This paper investigates how breather excitations induce loop structures in superfluid vortex filaments, revealing their formation conditions, dynamics, and energy relationships, thereby advancing understanding of vortex behavior and potential control mechanisms.

## Contribution

It introduces a physical quantity, the integral of the relative quadratic curvature, to characterize breather-induced vortex loops and establishes its linear correlation with loop size.

## Key findings

- Kuznetsov-Ma breather causes periodic vortex loops.
- Super-regular breather induces symmetric-breaking loop pairs.
- The integral of the relative quadratic curvature correlates linearly with loop size.

## Abstract

We study and characterize the breather-induced quantized superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised perturbations. Such vortex filaments, emerging from an otherwise perturbed helical vortex, exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the vortex. The loop induced by Kuznetsov-Ma breather emerges periodically as time increases, while the loop structure triggered by super-regular breather---the loop pair---exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of super-regular breather. In particular, we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity---the integral of the relative quadratic curvature---which corresponds to the effective energy of breathers. Although the nature of nonlinearity, it is demonstrated that this physical quantity shows a linear correlation with the loop size. These results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.