The statistical properties of the q-deformed Dirac oscillator in one and two-dimensions

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