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.