BEC and dimensional crossover in a boson gas within multi-slabs

TL;DR

This paper investigates how a periodic multi-slab structure influences Bose-Einstein condensation in an ideal boson gas, revealing a continuous decrease in critical temperature and a dimensional crossover from 3D to 2D as potential barriers increase.

Contribution

It introduces a model of boson gas in a multi-slabs Kronig-Penney potential and analyzes the effects on BEC transition temperature and dimensional crossover, highlighting new phase transition behaviors.

Findings

Critical temperature decreases with increasing barrier height and cell size.

Surface plot indicates a phase transition between BEC and non-BEC states.

Specific heat shows a crossover from 3D to 2D behavior.

Abstract

For an ideal Bose-gas within a multi-slabs periodic structure, we report a dimensional crossover and discuss whether a BEC transition at $T_c \neq 0$ disappears or not. The multi-slabs structure is generated via a Kronig-Penney potential perpendicular to the slabs of width $a$ and separated by a distance $b$. The ability of the particles to jump between adjacent slabs is determined by the hight $V_0$ and width $b$ of the potential barrier. Contrary to what happens in the boson gas inside a zero-width multilayers case, where the critical temperature diminishes and goes up again as a function of the wall separation, here the $T_c$ decreases continuously as the potential barrier height and the cell size $a+b$ increase. We plot the surface $T_c = 10^{-6}$ showing two prominent regions in the parameters space, which suggest a phase transition BEC-NOBEC at $T \neq 0$. %The position of the phase transition surface is almost independent of the ratio $r=b/a$ while the cell size $a+b$ is almost proportional to the square root of the height of the potential barriers. The specific heat shows a crossover from 3D to 2D when the height of the potential or the barrier width increase, in addition to the well known peak related to the Bose-Einstein condensation.