Finite-Range Corrections to the Thermodynamics of the One-Dimensional Bose Gas

TL;DR

This paper derives finite-range corrections to the thermodynamics of a one-dimensional Bose gas, extending the Lieb-Liniger model by including effects of the interaction potential's effective range at finite temperature.

Contribution

It introduces a beyond-mean-field equation of state accounting for finite-range effects, providing analytical expressions for thermodynamic quantities.

Findings

Thermodynamic quantities are modified by the ratio of effective range to scattering length.

Finite-range effects influence pressure and sound velocity in the 1D Bose gas.

Analytical results are obtained through dimensional regularization of quantum fluctuations.

Abstract

The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal corrections to this equation of state taking into account finite-range effects of the inter-atomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the one-dimensional Bose gas thermodynamic quantities like pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.