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The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings withtwo electrons has been studied and has been explained in an analytical way, theevolution of the period and amplitudes against the magnetic field can beexactly described. Furthermore, the dipole transition of the ground state wasfound to have essentially two frequencies, their difference appears as anoscillation matching the oscillation of the persistent current exactly. Anumber of equalities relating the observables and dynamical parameters havebeen found.

Coincidence of the oscillations in the dipole transition and in the persistent current of narrow quantum rings with two electrons