Critical temperature of extremely confined bosons

The critical BEC temperature $T_{c}$\ of an ideal boson gas inside a layered structure simulated by a Kronig-Penney-like trapping potential is found to {\it decrease} as the separation between planes decrease to the order of the thermal wavelength $\lambda _{0}\equiv h/\sqrt{2\pi mk_{B}T_0}$ of the free boson gas at its critical BEC temperature $T_{0}$ [1], where $m$ is the boson mass. However, when the plane separation is less than $\lambda _{0}$, $T_{c}$ increases to nearly $T_{0}$. This phenomenon could be present in cuprate superconductors and explain why their transition temperatures increases as a function of pressure. [1] P. Salas, M. Fortes, M. de Llano, F.J. Sevilla and M.A. Sol\'{\i}s, {\it ``Thermodynamic properties of bosons among Kronig-Penney layers,''} to be published. We acknowledge the partial support from grant PAPIIT IN1114708.