Universal behavior of the BEC critical temperature for a multislab ideal Bose gas

TL;DR

This paper investigates how a multi-slab periodic potential affects the critical temperature and dimensional crossover of an ideal Bose gas, revealing universal behavior and the impact of potential barriers on Bose-Einstein condensation.

Contribution

It demonstrates the universal inverse square root dependence of the critical temperature on barrier height and characterizes the dimensional crossover in specific heat due to potential barriers.

Findings

Critical temperature decreases with barrier height, inversely proportional to the square root for large barriers.

The critical temperature behavior is universal, independent of barrier width and spacing.

Specific heat shows a 3D to 2D crossover influenced by potential barrier parameters.

Abstract

For an ideal Bose-gas within a multi-slab periodic structure, we discuss the effect of the spatial distribution of the gas on its Bose-Einstein condensation critical temperature $T_c$, as well as on the origin of its dimensional crossover observed in the specific heat. The multi-slabs structure is generated by applying a Kronig-Penney potential to the gas in the perpendicular direction to the slabs of width $b$ and separated by a distance $a$, and allowing the particles to move freely in the other two directions. We found that $T_c$ decreases continuously as the potential barrier height increases, becoming inversely proportional to the square root of the barrier height when it is large enough. This behavior is {\it universal} as it is independent of the width and spacing of the barriers. The specific heat at constant volume 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. These features are due to the trapping of the bosons by the potential barriers, and can be characterized by the energy difference between the energy bands below the potential height.