Chern-Simons quantum mechanics and fractional angular momentum in atom system

TL;DR

This paper investigates a planar atom with an electric dipole interacting with magnetic fields, revealing that its reduced model exhibits fractional angular momentum and Chern-Simons-like spectra, highlighting unique quantum mechanical properties.

Contribution

It demonstrates that the reduced model of a planar atom can realize Chern-Simons quantum mechanics and fractional angular momentum simultaneously, with exact solutions and regularization methods.

Findings

Energy spectra of the reduced model differ from the full model without regularization.

Fractional angular momentum appears in the reduced model.

The model provides a physical realization of Chern-Simons quantum mechanics.

Abstract

The model of a planar atom which possesses a non-vanishing electric dipole moment interacting with magnetic fields in a specific setting is studied. Energy spectra of this model and its reduced model, which is the limit of cooling down the atom to the negligible kinetic energy, are solved exactly. We show that %similar with the Chern-Simons quantum mechanics, energy spectra of the reduced model can not be obtained directly from the full ones by taking the same limit. In order to match them, we must regularize energy spectra of the full model when the limit of the negligible kinetic energy is taken. It is one of the characteristics of the Chern-Simons quantum mechanics. Besides it, the canonical angular momentum of the reduced model will take fractional values although the full model can only take integers. It means that it is possible to realize the Chern-Simons quantum mechanics and fractional angular momentum simultaneously by this model.