Bose-Einstein Condensation in Narrow Channels

Abstract

The problem of the transition temperature of liquid helium in narrow channels has been considered by using the ideal Bose-Einstein gas as a model. It has been found that for a channel of square cross section ($D\times D$) and length $L$, the transition temperature $T_c$ is given by the expression $\frac{T_c}{T_{\mathrm{cB}}}=\left(0.84\mathrm{} {\AA }^{-1\mathrm{}}\right)\frac{D^2}{L}$ under the conditions that $\frac{D^2}{L}\ll \lambda$, where $\lambda$ is the thermal de Broglie wavelength, and $T_{\mathrm{cB}}$ is the transition temperature in the case of an infinite volume.