Determination of the second virial coefficient of interacting Bosons using the method of Wigner distribution function

TL;DR

This paper extends a Wigner distribution function method to calculate the second virial coefficient of interacting Bosons, providing a novel approach to quantum statistical properties of interacting quantum gases.

Contribution

It introduces a formalism using the Wigner distribution function to analyze interacting Bosons, specifically calculating the second virial coefficient with pairwise Lenard-Jones interactions.

Findings

Calculated the quantum second virial coefficient for interacting Bosons.

Compared results with previous methods and found consistency.

Demonstrated the applicability of the formalism to pairwise interactions.

Abstract

In a previous article \cite{kn:anirban1} a method has been introduced to derive the all order Bose-Einstein distribution of the non interacting Bosons as the solution of the Wigner equation. The process was a perturbative one where the Bose-Einstein distribution was taken as the unperturbed solution. In this article it is shown that the same formalism is also applicable in the case of interacting Bosons. The formalism has been applied to calculate the quantum second virial coefficient of the Bosons interacting pairwise via Lenard-Jones potential and compared with the previous result.