Superstatistical properties of the one-dimensional Dirac oscillator

Superstatistics of the one-dimensional Klein-Gordon oscillator with energy-dependent potentials

“…Recently, the superstatistical of the one-dimensional Dirac oscillator has been well studied [7]. Although arguments of the validity of applicability of law thermodynamics in superstatistics for both Dirac and Klein-Gordon equations are the same, the difference is very clear.…”

“…In our case, we are focused on Gamma distribution defined by Eq. (16): this choice is justified by the wide use of this distribution in the literature: as an example, we can cite the following: in blinking quantum dots, cosmic ray statistics, various scattering processes in particle physics [9], one-dimensional Dirac oscillator [7] and the thermo-magnetic properties of a system of 2D GaAs quantum dots [34]. Other recent applications of the superstatistics are briefly reviewed by Refs.…”

“…In our case, to seek simplicity, we use the approximation of the low-energy asymptotics (for more detail, see Ref. [7]). This approximation represents the leading order correction to ordinary statistical mechanics in our system with temperature fluctuations for small values of the energy E. More precisely, the low-energy asymptotics behavior is universal: that means that the generalized Boltzmann factor for a different choice of Superstatistics is expressed in terms of the universal parameters q and β 0 as follows:…”

“…In the local cells, local equilibrium statistical mechanics is then valid for the given β in that cell (for more detail see Ref. [7] and references therein). In conclusion, and following these arguments, it is possible to do ordinary statistical mechanics for this superstatistical non-equilibrium system, with all the known formulae such as described by Eqs.…”

“…The properties of these systems have become a topic of great interest in the last few years, and it has found many applications in several branches of physics (see Ref. [7] and references therein). It is known that Superstatistics is a branch of statistical mechanics or statistical physics that is devoted to the study of non-linear and non-equilibrium systems.…”