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

Kåre Olaussen, Asle Sudbø

Published 2015-02-04Version 1

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.