The 2D radial stationary nonlinear Schroedinger equation yields a new action-phase quantization of energy, in contrast with the linear case where the energy levels are degenerated with respect to the Ermakov constant. Characteristic values of radial energy quantization are given in the Gross–Pitaevskii mean-field description for the main vortex-nucleation experiments performed in rotating Bose–Einstein condensates. Finally, the link with Einstein’s conjecture about non-quantizability of quasiperiodic orbits on a 2D torus is pointed out.
Reinisch, G., "Radial action-phase quantization in Bose Einstein condensates", Physics Letters A, 372, pp. 769-774 (2008) (doi:10.1016/j.physleta.2007.08.060)