Density shift of Bose gas due to the Casimir effect and mean field potential

TL;DR

This paper systematically investigates how the density of a Bose gas is affected by the Casimir effect and mean field potential across different dimensions, revealing dimension-dependent roles of these effects on density and critical temperature shifts.

Contribution

It provides a comprehensive analysis of the combined and separate impacts of the Casimir effect and mean field potential on Bose gas density in arbitrary dimensions, highlighting the unique case of three dimensions.

Findings

In 3D, density shift is solely due to the Casimir effect.

For dimensions greater than 3, both Casimir and MFP influence density shift.

MFP causes a negative density shift and positive critical temperature shift when acting alone.

Abstract

The shift of density of Bose gas due to the mean field potential (MFP) and the Casimir effect is systematically investigated in the $d$-dimensional configuration space from the point of thermodynamic consideration. We show that, for $d=3$, the shift of density arises completely due to the Casimir effect and, the MFP remains totally ineffective regardless of the state, condensate or non-condensate. But for dimension $d>3$ the MFP plays an active role in shifting the density of Bose gas along with the Casimir interaction. The sign of density shift becomes positive in the present case. So, the corresponding critical temperature shift would be negative, because these two shifts are related as $\Delta n_{c}$/$n_{c}$ $\approx$ -$\Delta T_{c}$/$T_{c}$. It is important to note that, the MFP causes a shift of density for $d>3$ even when the Casimir effect is not there, and the sign of shift becomes negative then; consequently, the critical temperature shift would be positive with MFP alone in this particular situation.