Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Theoretical Physics

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

Zhiyu Luo, Qing xiang Wang, Xiao Li, Jian Jing

Published Feb 20, 2012• 18 citations
Publisher
DOI
10.1007/s10773-012-1094-x

Related papers

Two and k-Photon Jaynes–Cummings Models and Dirac Oscillator Problem in Bargmann–Segal Representation

H. Panahi, S. Asghari Rad

International Journal of Theoretical Physics•Jul 4, 2013•6 citations

The Schrödinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

E. S. Santos, G R de Melo

•Feb 1, 2011•0 citations

The Jaynes-Cummings Model in Phase Space Quantum Mechanics

Mar Sánchez–Córdova, Jasel Berra–Montiel, Alberto Molgado

arXiv:2506.23386•International Journal of Theoretical Physics•Jan 23, 2026•1 citation

Chirality quantum phase transition of a noncommutative planar Dirac oscillator

Yu-Long Hou, Qing Wang, Zi-Gang Yuan +2 more

A map from the charged Dirac oscillator on a noncommutative plane interacting with a homogeneous magnetic field onto a quantum optics model is proposed. We find that both anti-Jaynes-Cummings (AJC) and Jaynes-Cummings (JC) interactions are included in this mapped quantum optics model. A competition between AJC and JC interactions will happen when the intensity of the magnetic field changes. Contrary to previous studies, the competition is symmetrical since the phonons that take part in the competition are only associated with the excitation of the Dirac oscillator. Furthermore, this model will experience a quantum phase transition when the intensity of the magnetic field crosses the critical point. However, the critical point is different from the one in the model of the charged nonrelativistic harmonic oscillator interacting with a homogenous magnetic field on a noncommutative plane. It also deviates from its commutative counterpart because of spatial noncommutativity. Some characteristics of the quantum phase transition are studied. Then we investigate the nonrelativistic limit of this model. Our results show that its nonrelativistic counterpart inherits similar properties of the chirality quantum phase transition from the relativistic one.

Physical Review A•Mar 26, 2015•2 citations

Noncommutative 2+1 dimensional Dirac oscillator and quantum phase transition

Yu-Long Hou, Qing xiang Wang, Zheng‐Wen Long +1 more

Annals of Physics•Dec 13, 2014•7 citations

Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

Shao‐Hua Wang, Yu-Long Hou, Qing Wang +2 more

The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held 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 held) 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.

Communications in Theoretical Physics•Dec 1, 2014•0 citations
A map from the charged Dirac oscillator on a noncommutative plane interacting with a homogeneous magnetic field onto a quantum optics model is proposed. We find that both anti-Jaynes-Cummings (AJC) and Jaynes-Cummings (JC) interactions are included in this mapped quantum optics model. A competition between AJC and JC interactions will happen when the intensity of the magnetic field changes. Contrary to previous studies, the competition is symmetrical since the phonons that take part in the competition are only associated with the excitation of the Dirac oscillator. Furthermore, this model will experience a quantum phase transition when the intensity of the magnetic field crosses the critical point. However, the critical point is different from the one in the model of the charged nonrelativistic harmonic oscillator interacting with a homogenous magnetic field on a noncommutative plane. It also deviates from its commutative counterpart because of spatial noncommutativity. Some characteristics of the quantum phase transition are studied. Then we investigate the nonrelativistic limit of this model. Our results show that its nonrelativistic counterpart inherits similar properties of the chirality quantum phase transition from the relativistic one.
The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held 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 held) 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.