Fractional Quantum Hall Effect, Cranked Harmonic Oscillator, and Classical Periodic Orbits

TL;DR

This paper models the fractional quantum Hall effect using a rotated harmonic oscillator, predicting energy gaps that align with experimental data, and connects classical periodic orbits to quantum phenomena.

Contribution

It introduces a novel model linking a cranked harmonic oscillator to fractional quantum Hall states, providing quantitative predictions for energy gaps.

Findings

Predicted energy gap proportional to a n_e/pq for a=odd.

Model's predictions agree with recent experimental data.

Qualitative explanations support the model's effectiveness.

Abstract

A two-dimensional harmonic oscillator, when rotated by the oscillator frequency, generates Landau-like levels. A further cranking results in condensates and gaps resembling the fractional quantum Hall effect. For a filling fraction $\nu=p/q$, with $q$ odd, the model predicts that the gap is proportional to $\sqrt{n_{e}/pq}$, where $n_{e}$ is the electron density of the sample. This agrees well with recent experimental data. Qualitative arguments for the success of the model are given.