Boson thermodynamics in the gravity field

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.