Few-body collective excitations beyond Kohn's theorem in quantum Hall systems

TL;DR

This paper predicts a new collective excitation in quantum Hall systems called the hyperradial breathing mode, which depends on inter-particle interactions and can be observed in cold atom and quantum Hall experiments.

Contribution

It introduces the hyperradial breathing mode as a novel collective excitation beyond Kohn's theorem using a hyperspherical approach.

Findings

Hyperradial breathing mode depends on inter-particle interactions.

Mode's behavior differs under Coulomb and dipole-dipole interactions.

Potential observability in cold atom and quantum Hall experiments.

Abstract

A relative coordinate breathing mode in the quantum Hall system is predicted to exist with different behavior under either Coulomb or dipole-dipole interactions. While Kohn's theorem predicts that any relative coordinate interaction will fail to alter the center of mass energy spectrum, it can affect excitations in the relative coordinates. One such collective excitation, which we call the hyperradial breathing mode, emerges naturally from a few-body, hyperspherical representation of the problem and depends on the inter-particle interactions, the ground state wave function, and the number of particles participating in the excitation. Possible observations of this excitation will be discussed in the context of both cold rotating atomic simulations and conventional quantum Hall experiments.