Splitting of triply quantized vortices in Bose–Einstein condensates of finite temperature

Abstract Utilizing the dissipative Gross–Pitaevskii equation, we investigated the splitting dynamics of triply quantized vortices at finite temperature. Through linear perturbation analysis, we determined the excitation modes of these vortices across various dissipation parameters. We identified three unstable modes with p = 2-, 3- and 4-fold rotational symmetries, revealing a significant dynamic transition of the most unstable mode. That is, as the dissipation parameter increases the most unstable mode transitions from the p = 2 mode to the p = 3 mode. Throughout the entire range of dissipation parameters, the p = 4 unstable mode is never the dominant mode. Subsequently, we performed nonlinear numerical simulations of the vortex splitting process. Under random perturbations we confirmed the dynamical transition, and under specific perturbations we confirmed the instability of the p = 4 mode. Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.