Symmetry Breaking of Vortex Patterns in a Rotating Harmonic Potential

We numerically study the symmetry breaking instabilities of vortex patterns in a rotating harmonic potential using a type of Ginzburg-Landau equation. The configurations of vortex lattices change markedly by the symmetry-breaking instabilities, and then, some vortices move away from the confinement potential, which leads to the annihilation of vortices. The symmetry-breaking instabilities and the instabilities of vortex nucleation determine the parameter region of stable vortex patterns. We verify that the symmetry-breaking instabilities also occur in a type of complex Ginzburg-Landau equation.