Rotating electrons in quantum dots: Quantum Hall liquid in the classical limit

TL;DR

This paper compares quantum and classical models of electrons in quantum dots, showing that at low filling factors, quantum Hall liquids behave like classical vibrating localized electrons influenced mainly by the Coriolis force.

Contribution

It demonstrates that classical vibrations accurately describe low-energy excitations of quantum Hall liquids in quantum dots at low filling factors.

Findings

Quantum and classical results agree quantitatively.

Classical vibrations dominate low-energy excitations.

Coriolis force significantly influences vibration frequencies.

Abstract

We solve the problem of a few electrons in a two-dimensional harmonic confinement using quantum mechanical exact diagonalization technique, on one hand, and classical mechanics, on the other hand. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.