Nonlinear Excitation Dynamics Of Quantized Superfluid Vortices And Their Characterization

As the main degree of freedom of quantum fluid,the quantized superfluid vortex filament is a hot topic in the research of multi-body physics and photophysics.It is one of the important problems to discover new vortex structures and clarify their mechanism.The research on the nonlinear excitation dynamics in the quantized vortices is mainly limited to the structures and evolution processes of the vortex filaments corresponding to the N-soliton.A variety of vortex structures has obtained,which has enriched our knowledge of vortices and provided theoretical basis for controllable loop structure on the vortices.On the other hand,the types of nonlinear excitations have become more and more abundant as the research progressed;however,the influence of these nonlinear excitations on the quantized superfluid vortices is unknown.Therefore,in this paper,we mainly study the characteristics of these nonlinear waves on quantized vortices,and expect to find more vortex structures.In this paper,based on the Biot-Savart equation,we have focused on several nonlin-ear excitation dynamics processes and the evolution characteristics of quantized superfluid vortices through Hasimoto transformation and inverse transformation.The analysis of the curvature and torsion of these vortex filaments shows that there are two types of loop excita-tions in quantized vortices,and one of them is generated by the dual action of bending and twisting of the vortex filaments,which is represented by the vortex structures corresponding to Kuznetsov-Ma breather and super-regular breather.The further research demonstrates that for the vortex filaments corresponding to the Kuznetsov-Ma breather,the integral of the rela-tive quadratic curvature shows a linear correlation with the loop size;while the loop structure induced by the super-regular breather shows an interesting reflection symmetry breaking,and the degree of asymmetry is directly proportional to the background torsion|₀|.The axial flow effect is ubiquitous in quantum fluids,which increases the diversity of vortex filaments.This paper theoretically predicts three new vortex solitons induced by the axial flow effect in superfluid,and shows another mechanism of the loop structure through the analysis of curvature and torsion:the loop structure only originates from the bending action of curvature when the torsion is a constant.These studies not only deepen our understanding of the nonlinear excitation dynamics of quantized superfluid vortex filaments,but also contribute to the controllable ring-like excitations on the vortices.