Dynamics of the breathing mode with rotational symmetry in two-dimensional Bose–Einstein condensates

Symmetry is crucial for both equilibrium properties and non-equilibrium dynamics. We study the breathing-mode dynamics in two-dimensional Bose–Einstein condensates (BECs) with rotational symmetry. Gross–Pitaevskii simulations and stability analysis show that initial states with different rotational symmetries exhibit distinct dynamical behaviors. However, the dominant oscillation frequencies of |〈ψ(0)|ψ(t)〉| consistently appear approximately as multiples of 0.5ω. The evolution of perturbations displays a consistent dynamical pattern: an initial linear increase, followed by a transition to power-law growth at a symmetry-dependent timescale. The power-law exponent decreases at higher rotational symmetry, indicating enhanced robustness. These features can be interpreted by a three-stage evolution of the perturbation profiles: (i) diffusion from the initial shape across the condensate domain, (ii) approximate synchronized motion with the underlying BEC breathing dynamics, and (iii) further diffusion leading to irregularity in the condensate. Furthermore, the maximal Lyapunov exponent approaches zero, suggesting the existence of stable non-chaotic structures or quasi-periodic orbits in the vicinity of these breathing modes. Our results reveal that the collective dynamics and stability of quantum fluids can be controlled by jointly engineering initial-state symmetry and boundary conditions, offering new pathways for manipulating far-from-equilibrium behavior in ultracold gases.