Symmetry background of the fractional Aharonov-Bohm oscillation and an   oscillation in dipole-transitions of narrow quantum rings with a   few-electrons
  The low-lying spectrum of a 3-electron narrow ring has been analyzed analytically. A phase-diagram for the ground state band against the magnetic field and the radius of the ring is obtained. The symmetry background of the fractional Aharonov-Bohm oscillation has been revealed. A very strong oscillation in the dipole transition is found. The discussion can be generalized to N-electron rings. 
C. G. Bao, G.M.Huang, Y.M. Liu