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

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 t...

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Bibliographic Details
Published in:arXiv.org 2017-02
Main Authors: Majari, Parisa, Alfredo, Luis, Setare, Mohammad Reza
Format: Article
Language:English
Subjects:
Angular momentum
Collapse
Deformation effects
Mapping
Relativism
Relativistic effects
Two dimensional models
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1702.03077