Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches

Hadi Sobhani,Won Sang Chung,Hassan Hassanabadi

doi:10.1140/epjc/s10052-018-5581-y

Abstract

In this article, we determine the thermodynamical properties of the anharmonic canonical ensemble within the cosmic-string framework. We use the ordinary statistics and the q-deformed superstatistics for this study. The q-deformed superstatistics is derived by modifying the probability density in the original superstatistics. The Schrödinger equation is rewritten in the cosmic-string framework. Next, the anharmonic oscillator is investigated in detail. The wave function and the energy spectrum of the considered system are derived using the bi-confluent Heun functions. In the next step, we first determine the thermodynamical properties for the canonical ensemble of the anharmonic oscillator in the cosmic-string framework using the ordinary statistics approach. Also, these quantities have been obtained in the q-deformed superstatistics. For vanishing deformation parameter, the ordinary results are obtained.

Highlights

Topological defects were first theorized by Kibble [1]
A α and considering the wave function (t, r) = exp [i(−εt + lφ + kz)] (ρ) we obtain in which the angular parameter is associated to cosmic string space-time represented by α, that is, α
We are ready to investigate some thermodynamical properties from a statistical mechanics point of view

Summary

Introduction

Topological defects were first theorized by Kibble [1]. These defects are physical structures produced in symmetrybreaking phase transitions in the early universe. Among all the possible types of defects, the one-dimensional cosmic strings are the focus of most of the studies in this area [2] This is because of the compatibility with the current cosmological models and their association with several brane inflation scenarios [3,4] and super-symmetric grand unified theories [5]. Where f (β , β) is a probability density and, according to the definition (1.1), this is an average of the ordinary Boltzmann factor. We first intend to modify the probability density and discuss the thermodynamical proprieties of the anharmonic oscillator ensemble within the cosmic-string framework. 2, the probability density is modified and the new effective Boltzmann factor is derived. In the other subsection, considering the modified form of the probability density we will obtain thermodynamical properties of the system. Page 3 of 9 106 work considering the anharmonic oscillator to obtain thermodynamical properties

Schrödinger equation within cosmic-string framework

Thermodynamical properties within cosmic-string framework

Conclusions