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

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

1993-07-19

arxiv.org/abs/cond-mat/9307041v1

Physics

Condensed Matter

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

Scientific paper

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.

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