Analytical theory of enhanced Bose-Einstein condensation in thin films

Abstract

We present an analytically solvable theory of Bose-Einstein condensation in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-to-moderate confinement regime (where the film thickness $L$ is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature $T_{c} \sim L^{-1/2}$. For cold Bose gases, this implies an enhancement up to two orders of magnitude in $T_{c}$ for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. $C \sim T^{2}$, is predicted for nano-scale films, which implies a different $\lambda$ point behaviour with respect to bulk systems, while the condensate fraction is predicted to follow a $[1- (T/T_{c})^{2}]$ law.