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

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...

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Bibliographic Details
Published inPhysics letters. B Vol. 659; no. 5; pp. 906 - 912
Main Authors Alvarez, Pedro D., Gomis, Joaquim, Kamimura, Kiyoshi, Plyushchay, Mikhail S.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 07.02.2008
Elsevier Science
Subjects
Exact sciences and technology
Nuclear physics
Physics
The physics of elementary particles and fields
Spectral properties
Particle models
Harmonic oscillators
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Summary: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.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2007.12.016