Partition Function for a 1-D delta-function Bose Gas

TL;DR

This paper explicitly calculates the N-particle partition function for a one-dimensional delta-function Bose gas using the Bethe ansatz, confirming the consistency with the thermal Bethe ansatz method.

Contribution

It provides an explicit calculation of the partition function using only the periodic boundary condition, aligning with the thermal Bethe ansatz results.

Findings

Partition function explicitly calculated for 1D delta Bose gas

Cluster integrals match those from thermal Bethe ansatz

Validates Bethe ansatz approach for thermodynamic properties

Abstract

The N-particle partition function of a one-dimensional $\delta$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as those by the thermal Bethe ansatz method.