Critical Temperature of Bose-Einstein Condensation of Hard Sphere Gases

Abstract

We determine the critical temperature of a 3-d homogeneous system of hard-sphere Bosons by path-integral Monte Carlo simulations and finite-size scaling. At low densities, we find that the critical temperature is increased by the repulsive interactions, in the form of a power law in density with exponent 1/3: $\Delta T_C/T_0\sim (n{a}^3{)}^{1/3}$. At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.

4 pages, 4 figures;; replacement with minor corrections: p.1 (after Eq.1), p.2 (after Eq. 4), x-axis label in Fig. 2

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