Superstatistical properties of the one-dimensional Dirac oscillator

Abstract

In this paper, we consider the thermal properties of one-dimensional Dirac in the framework of the theory of superstatistics where the probability density f(β) follows χ2−superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated by using both Mellin Transformation and Zeta function. This approximation leads to a universal parameter q for any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameter q. As an application, we extend this concept to the case of Graphene: the reason of this choice is due the existence of an exact mapping about the Dirac oscillator and the compound in question.