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

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.

13p (9 pages for the text and 4 figures)