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

Pedro D. Alvarez; Joaquim Gomis; Kiyoshi Kamimura; Mikhail S. Plyushchay

doi:10.1016/j.physletb.2007.12.016

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

Pedro D. Alvarez, Joaquim Gomis, Kiyoshi Kamimura, Mikhail S. Plyushchay^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

66 Scopus citations

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.

Original language	English
Pages (from-to)	906-912
Number of pages	7
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	659
Issue number	5
DOIs	https://doi.org/10.1016/j.physletb.2007.12.016
State	Published - 2008
Externally published	Yes

ASJC Scopus subject areas

Nuclear and High Energy Physics

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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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AU - Gomis, Joaquim

AU - Kamimura, Kiyoshi

AU - Plyushchay, Mikhail S.

PY - 2008/2/7

Y1 - 2008/2/7

N2 - 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.

AB - 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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JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

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

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