Dimensional crossover of a boson gas in multilayers

Details Dimensional crossover of a boson gas in multilayers Dimensional crossover of a boson gas in multilayers

2010-07-08

arxiv.org/abs/1007.1458v1

Physics

Condensed Matter

Quantum Gases

Ten pages, nine figures

Scientific paper

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 $TT_{c}$, it is evidenced by a broad minimum in $C_{V}(T)$.

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