# Dimensional crossover of a boson gas in multilayers - Condensed Matter > Quantum Gases

Abstract: We obtain the thermodynamic properties for a non-interacting Bose gasconstrained on multilayers modeled by a periodic Kronig-Penney delta potentialin one direction and allowed to be free in the other two directions. We reportBose-Einstein condensation BEC critical temperatures, chemical potential,internal energy, specific heat, and entropy for different values of adimensionless impenetrability $P\geqslant 0$ between layers. The BEC criticaltemperature $T {c}$ coincides with the ideal gas BEC critical temperature$T {0}$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity forany finite interlayer separation. The specific heat $C {V}$ \textit{vs} $T$ forfinite $P$ and plane separation $a$ exhibits one minimum and one or two maximain addition to the BEC, for temperatures larger than $T {c}$ which highlightsthe effects due to particle confinement. Then we discuss a distinctivedimensional crossover of the system through the specific heat behavior drivenby the magnitude of $P$. For $TT {c}$, it is evidenced by a broadminimum in $C {V}T$.

Author: P. Salas, F.J. Sevilla, M. Fortes, M. de Llano, A. Camacho, M.A. Solís

Source: https://arxiv.org/