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 twofold rotational symmetry mode to the threefold one, followed by a transition from the threefold one to the fourfold one at a higher temperature. As the temperature is increased, we also observe the fivefold and sixfold rotational symmetry unstable modes get excited successively. Employing the full nonlinear numerical simulations, we further demonstrate that these two novel dynamical transitions, along with the temperature-induced instabilities for the fivefold and sixfold 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.

Figure 1

(a) The configuration of a quadruply quantized vortex at temperature $T/T_c=0.636$. (b) The low lying spectrum of quasinormal modes ($\omega$) for $p=2$ of the vortex in the upper panel.

Figure 2

The variation of the imaginary part of the dominant mode of the quadruply quantized vortex with the temperature for $p=2$, 3, 4, 5, 6.

Figure 3

Density and phase plots of the condensate for splitting processes of the quadruply quantized vortex under random perturbations with distinct splitting patterns at different temperatures.

Figure 4

Density and phase plots of the condensate for splitting processes of the quadruply quantized vortex under $p=5$, 6 type perturbations at temperature $T/T_c=0.931$, where six vortices are clearly seen to surround two antivortices from the close-up of the phase plot.