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

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.

12 pages

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Cited by in corpus (49)

• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Conformal mechanics in Newton-Hooke spacetime
• Noncommutative oscillator, symmetry and Landau problem
• Exotic galilean symmetry and non-commutative mechanics
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
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• Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
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• Conformal Anisotropic Mechanics
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