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 ($D\ifmmode\times\else\texttimes\fi{}D$) and length $L$, the transition temperature ${T}_{c}$ is given by the expression $\frac{{T}_{c}}{{T}_{\mathrm{cB}}}=(0.84 {\AA{}}^{\ensuremath{-}1})\frac{{D}^{2}}{L}$ under the conditions that $\frac{{D}^{2}}{L}\ensuremath{\ll}\ensuremath{\lambda}$, where $\ensuremath{\lambda}$ is the thermal de Broglie wavelength, and ${T}_{\mathrm{cB}}$ is the transition temperature in the case of an infinite volume.