Heating up quadruply quantized vortices: Splitting patterns and dynamical transitions

Using holographic duality, we investigate the impact of finite temperature on the instability and splitting patterns of quadruply quantized vortices, providing the first-ever analysis in this context. Through linear stability analysis, we reveal the occurrence of two consecutive dynamical transitions. At a specific low temperature, the dominant unstable mode transitions from the $2$-fold rotational symmetry mode to the $3$-fold one, followed by a transition from the $3$-fold one to the $4$-fold one at a higher temperature. As the temperature is increased, we also observe the $5$ and $6$-fold rotational symmetry unstable modes get excited successively. Employing the full non-linear numerical simulations, we further demonstrate that these two novel dynamical transitions, along with the temperature-induced instabilities for the $5$ and $6$-fold rotational symmetry modes, can be identified by examining the resulting distinct splitting patterns, which offers a promising route for the experimental verification in the cold atom gases.