Mapping of the 2 + 1 q-deformed Dirac oscillator onto the q-deformed Jaynes-Cummings model

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. 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