Bose-Einstein Condensation in Thin Films

Abstract

An asymptotic evaluation of the specific heat of an ideal Bose gas confined to a thin-film geometry ($\infty \times \infty \times D$) is carried out, under a variety of boundary conditions, without converting summations into integrations. The theoretical results for the Dirichlet boundary conditions (${\psi }_S=0\mathrm{}$) contain all the significant features of the numerical results obtained earlier by Goble and Trainor; in particular, we reproduce the characteristic length $D^{*}$ at which the specific heat of the system is at an absolute maximum. It turns out that $D^{*}$ is directly proportional to the mean interparticle distance $\overline{l}$, with a constant of proportionality $c(\approx 20-30)$. No such characteristic length appears if boundary conditions other than Dirichlet's are employed. The shift, and the rounding off, of the specific-heat maximum are also studied, and the distinguishing influence of the boundary conditions examined.