We present an analytically solvable theory of Bose–Einstein condensation (BEC) 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 ∼ 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 ∼ T ², is predicted for nano-scale films, which implies a different λ-point behavior with respect to bulk systems, while the condensate fraction is predicted to follow a [1−(T/Tc)2] law.

中文翻译：

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薄膜中增强玻色-爱因斯坦凝聚的解析理论

我们提出了薄膜几何中玻色-爱因斯坦凝聚 (BEC) 的解析可解理论。在低到中等限制条件下（其中薄膜厚度大号为微米量级）以及厚度为几纳米或更小的强限制区域。在强约束极限下预测高温 BEC 的可能性，临界温度的平方根散度吨 _c～大号 ^-1/2。对于冷 Bose 气体，这意味着增强高达两个数量级吨 _c用于纳米尺度的薄膜。还获得了热容量和冷凝物分数的分析预测。凝结水热容量的新定律，即C～吨 ²，预测为纳米级薄膜，这意味着不同的λ- 相对于散装系统的点行为，而凝析油部分预计遵循 [1个−(吨/吨C)2个] 法律。