Mapping of the 2+1 q-deformed Dirac oscillator onto the q-deformed Jaynes-Cummings model: It's non-relativistic limit and Zitterbewegung effect

Abstract

We develop the equivalence between the two-dimensional Dirac oscillator and the anti-Jaynes-Cummings model within a q-deformed scenario. We solve the Hamiltonian spectrum and the time evolution for number and coherent initial states, focusing on the appearance of the Zitterbewegung effect. We show the lack of preservation of the q-deformed versions of the total angular momentum that reproduces a collapse-revival structure. We provide suitable relations for the non relativistic limit.

7 pages, 2 figures

References in corpus (3)

• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Non-relativistic limit in the 2+1 Dirac Oscillator: A Ramsey Interferometry Effect
• Time-dependent q-deformed coherent states for generalized uncertainty relations

Cited by in corpus (5)

• Anomalous Floquet tunneling in uniaxially strained graphene
• Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
• Photonic realization of the deformed Dirac equation via the segmented graphene nanoribbons under inhomogeneous strain
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Photonic realization of the kappa-deformed Dirac equation