Fractional Quantum Hall Effect, Cranked Harmonic Oscillator, and Classical Periodic Orbits
R. K. Bhaduri, Shuxi Li, Kaori Tanakaa, J. C. Waddington
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 ν=p/q, with q odd, the model predicts that the gap is proportional to ne/pq, where ne is the electron density of the sample. This agrees well with recent experimental data. Qualitative arguments for the success of the model are given.
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