Quantum Statistics of Ideal Gases in Two Dimensions

Abstract

It is shown that in two dimensions the specific heat $C_V(T, N)$ for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all $T$ and $N$. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: $n=2\mathrm{}$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1\mathrm{}$.