Bose-Einstein condensation in non-uniform rotation

In this work, we study Bose-Einstein condensation in a system where the rotation frequency decreases radially from the center. The system is described by a modified Gross-Pitaevskii equation that includes a non-uniform rotation term controlled by a parameter λ, with the length scale of the rotation variation fixed relative to the healing length. The results show behavior distinctly different from the uniformly rotating condensate. In the uniform case a triangular vortex lattice forms, whereas here we observe that above a critical value λ c the vortices arrange themselves into a circular ring-shaped pattern near the boundary. Below λ c , the vortex configuration is disordered, lacking both triangular symmetry and a clear ring structure. The energy and chemical potential exhibit a sharp change at λ c , signaling a structural phase transition. A phase diagram is presented for the transition from the disordered to the ring-shaped vortex arrangement. The findings are discussed in the context of current experiments on synthetic gauge fields and structured rotation.