A mapping-independent analysis for the spectra of the non-commutative two-dimensional harmonic oscillator

Jing, Jian; Ma, Jun; Guo, Yong-Hong; Chen, Jianfeng

doi:10.1140/epjc/s10052-008-0682-7

Cited by 13 publications

(8 citation statements)

References 24 publications

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“…The energy spectra of the model ( 1) have been given in Eqs. (19) and (22). For the sake of clarities, we depict them in Fig.…”

Section: Degeneracy Of Energy Levelsmentioning

confidence: 99%

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Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

Wang¹,

Hou²,

Wang³

et al. 2014

Commun. Theor. Phys.

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The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic field is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti-Jaynes-Cummings (AJC) or Jaynes-Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic field) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit.

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“…The energy spectra of the model ( 1) have been given in Eqs. (19) and (22). For the sake of clarities, we depict them in Fig.…”

Section: Degeneracy Of Energy Levelsmentioning

confidence: 99%

“…[18] In Refs. [19]- [21], the spectra of some nonrelativistic models are solved by employing path integral formulation. Compared with the non-relativistic NCQM, relativistic NCQM attracts less attention.…”

Section: Introductionmentioning

confidence: 99%

Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

Wang¹,

Hou²,

Wang³

et al. 2014

Commun. Theor. Phys.

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“…Non-commutative quantum mechanics (NCQM) has also been studied extensively [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Some exactly solvable models, such as noncommutative harmonic oscillator and noncommutative Landau problems are studied.…”

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confidence: 99%

Dirac Oscillator in Noncommutative Phase Space and (Anti)-Jaynes-Cummings Models

Luo

Wang

et al. 2012

Int J Theor Phys

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We study planar Dirac oscillator in noncommutative phase space. The model is solved exactly. The relation between this model and Jaynes-Cummings (JC) or anti-JaynesCummings (AJC) models is investigated. We find that the behaviors of this model depend qualitatively on the signs of a dimensionless parameter κ. For a negative κ, we find that there is a map from this model to a model which contains only AJC terms. However, for a positive κ, there is a map from this model to a model which contains both AJC and JC terms simultaneously. Our investigation may afford a new way to study the noncommutative Dirac oscillator by means of quantum optics method, and vice verse.

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“…In order to answer the question of whether these different models in ordinary phase space share unique spectra, a mapping-independent method by employing path integral formulation is proposed in Refs. [21][22][23].…”

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confidence: 99%

2+1 Dimensional Noncommutative Dirac Oscillator and (Anti)-Jaynes-Cummings Models

et al. 2011

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We study Dirac oscillator in 2 + 1 dimensional noncommutative space. The model is solved exactly and the relationship with Jaynes-Cummings (JC) or anti-Jaynes-Cummings (AJC) models are investigated. We find that for a positive noncommutative parameter, there is an exact map from the 2 + 1 dimensional noncommutative Dirac oscillator to AJC model. However, for a negative noncommutative parameter, the noncommutative planar Dirac oscillator contains both AJC and JC terms simultaneously. Our investigation may afford a new way to study relativistic quantum mechanics models in noncommutative space by means of quantum optics method, and vice verse.

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A mapping-independent analysis for the spectra of the non-commutative two-dimensional harmonic oscillator

Cited by 13 publications

References 24 publications

Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

Dirac Oscillator in Noncommutative Phase Space and (Anti)-Jaynes-Cummings Models

2+1 Dimensional Noncommutative Dirac Oscillator and (Anti)-Jaynes-Cummings Models

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