Universal Behavior of the BEC Critical Temperature for a Multi-slab Ideal Bose Gas

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.