Energy spectrum and specific heat of a two-dimensional interacting Bose gas

The specific heat and the elementary excitation spectrum of a hard-sphere two-dimensional Bose gas is calculated assuming that only collective modes contribute to the thermodynamical properties of the fluid, at low temperatures. The calculation is based on the self-consistent-field approximation method with only one parameter adjustable, the hard-core diameter. The theoretical curve of the specific heat fits very well the experimental data of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ film at density of 0.0279 ${\mathrm{\AA }}^{-2\mathrm{}}$. The energy spectrum obtained in this work, which is qualitatively similar to the three-dimensional version, indicates the possibility of occurrence of superfluidity in such films.