Properties of the Virial Expansion and Equation of State of Ideal Quantum Gases in Arbitrary Dimensions

Abstract

The virial expansion of ideal quantum gases reveals some interesting and amusing properties when considered as a function of dimensionality $d$. In particular, the convergence radius $\rho_c(d)$ of the expansion is particulary large at {\em exactly\/} $d=3$ dimensions, $\rho_c(3) = 7.1068\ldots \times \lim_{d\to3} \rho_c(d)$. The same phenomenon occurs in a few other special (non-integer) dimensions. We explain the origin of these facts, and discuss more generally the structure of singularities governing the asymptotic behavior of the ideal gas virial expansion.