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

TL;DR

This paper investigates the eigenvalues of q-deformed Dirac oscillators in one and two dimensions, analyzing their properties, connections to quantum optics, and thermal behavior, including implications for relativistic quantum dynamics and graphene.

Contribution

It introduces a method using q-deformed creation and annihilation operators for solving the eigenvalues and explores the effects of q-deformation, including thermal properties and applications to graphene.

Findings

Eigenvalues are influenced by q-numbers and deformation parameter.

Established a connection between q-oscillators and quantum optics.

Derived thermal quantities and discussed implications for relativistic dynamics and graphene.

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