High density equation of state and condensation of ideal Bose gas using Mayer’s generating function

Suresh THELAKKADAN PUTHIYAVEETTIL,Udayanandan KANDOTH MURKOTH

doi:10.3906/fiz-1806-19

Abstract

The equation of state of an ideal collection of bosons in the low-density and high-density regime are found using the method of cluster expansion with Mayer's generating function. The saturation density and the other thermodynamic properties are calculated by the application of Mayer's convergence of the partition function. By calculating the value of saturation density from the singularity of the partition function series, the differences between the Mayer series convergence and the virial series convergence for ideal bosons are also established.

Highlights

The equation of state and the thermodynamic properties of the ideal quantum systems, like Bose or Fermi, show significant deviation from the ideal behavior [1]. This can be explained with the help of the quantum statistical method by considering the symmetric and antisymmetric properties of the wave functions
Bosons show a peculiar attractive spatial correlation, which can lead to a condensation [2,3] due to the symmetric nature of the wave functions, and fermions show repulsive spatial correlations due to the antisymmetric wave functions
Bose–Einstein condensation phenomenon was discussed using cluster expansion and Mayer’s convergence method using the generating function provided by Mayer

Summary

Introduction

The equation of state and the thermodynamic properties of the ideal quantum systems, like Bose or Fermi, show significant deviation from the ideal behavior [1]. This can be explained with the help of the quantum statistical method by considering the symmetric and antisymmetric properties of the wave functions. Fuchs proved that the radius of convergence (R0=ρ0λ3) of ideal Bose gas virial series in density is 12.56 ≤R0≤ 27.73 , and the other above mentioned calculations give values within the. All these show that the radius of convergence of the virial equation of state in density of ideal.

Cluster theory with Mayer’s generating function

Equation of state and Bose–Einstein condensation

Discussion and conclusions