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

## TL;DR

This paper analytically studies the fractional Aharonov-Bohm oscillations in narrow two-electron quantum rings, revealing a coincidence between dipole transition oscillations and persistent current variations.

## Contribution

It provides an exact analytical description of FABO evolution and uncovers the precise relationship between dipole transition frequencies and persistent current oscillations.

## Key findings

- FABO period and amplitude evolution are exactly described
- Dipole transition frequencies are essentially two and match persistent current oscillations
- Derived equalities relate observables and dynamical parameters

## Abstract

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