Fractional Quantum Hall Effect, Cranked Harmonic Oscillator, and Classical Periodic Orbits
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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 $ν=p/q$, 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)
13p (9 pages for the text and 4 figures)