Equation of state of Bose gases beyond the universal regime

TL;DR

This study uses diffusion Monte Carlo calculations to explore the equation of state of dilute Bose gases beyond the universal regime, considering effects of additional scattering parameters and proposing an analytical law for energy predictions.

Contribution

It provides the first detailed analysis of Bose gases beyond the universal regime, incorporating effective range and p-wave scattering effects with an analytical energy law.

Findings

Universality holds for small effective range up to gas parameters of 10^{-2}.

Increasing effective range reduces the universal regime and reveals p-wave effects.

An analytical law accurately reproduces the exact energies in the universal regime.

Abstract

The equation of state of dilute Bose gases, in which the energy only depends on the $s$-wave scattering length, is rather unknown beyond the universal limit. We have carried out a bunch of diffusion Monte Carlo calculations up to gas parameters of $10^{-2}$ to explore how the departure from the universality emerges. Using different model potentials, we calculate the energies of the gas in an exact way, within some statistical noise, and report the results as a function of the three relevant scattering parameters: the $s$-wave scattering length $a_0$, the $s$-wave effective range $r_0$, and the $p$-wave scattering length $a_1$. If the effective range is not large we observe universality in terms of $a_0$ and $r_0$ up to gas parameters of $10^{-2}$. If $r_0$ grows the regime of universality in these two parameters is reduced and effects of $a_1$ start to be observed. In the $(a_0,r_0)$ universal regime we propose an analytical law that reproduces fairly well the exact energies.