Lamb Shift of Energy Levels in Quantum Rings

TL;DR

This paper investigates the Lamb shift in quantum rings, revealing how it varies with quantum number, magnetic flux, and ring size, with potential measurable effects in organic molecules.

Contribution

It provides the first detailed analysis of vacuum radiative corrections to energy levels in quantum rings, including flux dependence and size effects.

Findings

Lamb shift increases with magnetic quantum number m in quantum rings.

Lamb shift exhibits magnetic-flux-dependent oscillations.

Shift magnitude varies significantly with ring radius, being measurable in organic molecules.

Abstract

We study the vacuum radiative corrections to energy levels of a confined electron in quantum rings. The calculations are provided for the Lamb shift of energy levels in low-momentum region of virtual photons and for both one-dimensional and two-dimensional quantum rings. We show that contrary to the well known case of a hydrogen atom the value of the Lamb shift increases with the magnetic momentum quantum number m. We also investigate the dependence of the Lamb shift on magnetic flux piercing the ring and demonstrate a presence of magnetic-flux-dependent oscillations. For one-dimensional ring the value of the shift strongly depends on the radius of the ring. It is extremely small for semiconductor rings but can attain measurable quantities in natural organic ring-shape molecules, such as benzene, cycloalcanes and porphyrins.