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Advances in High Energy Physics
Volume 2017 (2017), Article ID 9371391, 12 pages
Research Article

The Statistical Properties of the -Deformed Dirac Oscillator in One and Two Dimensions

1Laboratoire de Physique Appliquée et Théorique, Université Larbi Tébessi, Tébessa, Algeria
2Physics Department, Shahrood University of Technology, Shahrood, Iran

Correspondence should be addressed to Abdelmalek Boumali

Received 23 January 2017; Accepted 11 June 2017; Published 16 July 2017

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2017 Abdelmalek Boumali and Hassan Hassanabadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We study the behavior of the eigenvalues of the one and two dimensions of -deformed Dirac oscillator. The eigensolutions have been obtained by using a method based on the -deformed creation and annihilation operators in both dimensions. For a two-dimensional case, we have used the complex formalism which reduced the problem to a problem of one-dimensional case. The influence of the -numbers on the eigenvalues has been well analyzed. Also, the connection between the -oscillator and a quantum optics is well established. Finally, for very small deformation , we (i) showed the existence of well-known -deformed version of Zitterbewegung in relativistic quantum dynamics and (ii) calculated the partition function and all thermal quantities such as the free energy, total energy, entropy, and specific heat. The extension to the case of Graphene has been discussed only in the case of a pure phase ().