Boson thermodynamics in the gravity field

TL;DR

This paper investigates the effects of a uniform gravitational field on Bose-Einstein condensation, demonstrating that BEC is suppressed due to spectral discreteness and finite energy differences, with implications for experimental setups.

Contribution

It introduces the approximate continuous limit (ACL) to analyze BEC suppression under gravity, highlighting the role of finite energy gaps between quantum and classical ground states.

Findings

BEC is forbidden in a uniform gravitational field due to spectral discreteness.

The finite difference between quantum and classical ground levels prevents BEC in the ACL.

Comparison with experiments shows differences between rigid-wall and harmonic trap confinements.

Abstract

A uniform force like the weight has been shown to forbid Bose-Einstein condensation (BEC), due to the discreteness of the Airy spectrum, resulting from the weight. We show that BEC is forbidden even if the Airy spectrum is treated as continuous, in what we call the approximate continuous limit (ACL). The absence of BEC is due to the finite difference $\epsilon_0$ between the quantum and the classical ground level. A thorough study is made, showing the way the Bose-Einstein condensate grows, at temperatures lower than the fictious BEC temperature $T_f$, resulting from the limit $\epsilon_0\rightarrow0$. A comparison with some experimental data shows the difference between the confinement in a rigid-wall reservoir and in a harmonic trap.