Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magneticeld 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 ¯nd 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 ³ (which is the function of the intensity of the magnetic ¯eld) takes values in di®erent regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ³ 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 ¯nd that a similar chirality quantum phase transition takes place in its non-relativistic limit