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

R. K. Bhaduri·Shuxi Li·Kaori Tanakaa·J. C. Waddington
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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 $\sqrt{n_{e}/pq}$, 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.

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R. K. Bhaduri, Shuxi Li, Kaori Tanakaa, J. C. Waddington. 1993-07-19. Fractional Quantum Hall Effect, Cranked Harmonic Oscillator, and Classical Periodic Orbits. https://arxiv.org/abs/cond-mat/9307041

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