Dimensional crossover of a boson gas in multilayers

TL;DR

This paper studies how a non-interacting Bose gas in multilayer structures exhibits a dimensional crossover in thermodynamic behavior, especially in specific heat, as interlayer coupling varies from zero to strong.

Contribution

It provides a detailed analysis of the thermodynamic properties and dimensional crossover of a Bose gas constrained in multilayers modeled by a Kronig-Penney potential, highlighting the effects of interlayer coupling.

Findings

Critical temperature equals ideal gas BEC temperature at zero interlayer coupling.

Specific heat shows minima and maxima indicating confinement effects.

Dimensional crossover is driven by the interlayer coupling parameter P.

Abstract

We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P\geqslant 0$ between layers. The BEC critical temperature $T_{c}$ coincides with the ideal gas BEC critical temperature $T_{0}$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity for any finite interlayer separation. The specific heat $C_{V}$ \textit{vs} $T$ for finite $P$ and plane separation $a$ exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than $T_{c}$ which highlights the effects due to particle confinement. Then we discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of $P$. For $T<T_{c}$ the crossover is revealed by the change in the slope of $\log C_{V}(T)$ and when $T>T_{c}$, it is evidenced by a broad minimum in $C_{V}(T)$.