Effect of boundary conditions on finite Bose-Einstein assemblies

Abstract

The specific heat of an ideal semi-infinite ($\infty \times \infty \times D$) Bose gas is calculated numerically using a number of boundary conditions. The results provide a suitable comparison with the analytical calculations of Fisher and Barber and of Pathria. The agreement is very good except for the Neumann boundary condition where the numerical result shows deviation from that of Pathria. However, the earlier assumption of the existence of a "correlation length" appears to have little physical basis. For the hard-wall case, the anomaly in the specific heat is probably due to constraint on particle density. The distinctive effect of such a boundary condition (${\Psi }_s=0\mathrm{}$) is explored more thoroughly in maximal assemblies ($L\times L\times D$) where its effect on specific heat shows up prominently.