Equation of state for the one-dimensional attractive \delta-potential Bose gas in the weak-coupling regime

TL;DR

This paper derives an approximate equation of state for a one-dimensional attractive Bose gas with weak interactions, showing it behaves like a van der Waals gas at high temperatures, and provides formulas for the energy spectrum.

Contribution

It introduces approximate formulas for the quasi-momentum and energy spectrum, leading to a novel high-temperature equation of state for the weakly attractive Bose gas.

Findings

Equation of state resembles van der Waals without volume correction

Provides approximate formulas for quasi-momentum and energy spectrum

Applicable in the high-temperature regime

Abstract

Approximated formulae for real quasi-momentum and the associated energy spectrum are presented for one-dimensional Bose gas with weak attractive contact interactions. On the basis of the energy spectrum, we obtain the equation of state in the high temperature region, which is found to be the van der Waals equation without volume correction.