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arXiv · 0711.2644

Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry

Pedro D. Alvarez·Joaquim Gomis·Kiyoshi Kamimura·Mikhail S. Plyushchay
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Abstract

We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties.

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Pedro D. Alvarez, Joaquim Gomis, Kiyoshi Kamimura, Mikhail S. Plyushchay. 2007-11-16. Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry. https://doi.org/10.1016/j.physletb.2007.12.016

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