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: $n=2$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1$ .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: $n=2$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1$.

Physical ReviewSep 14, 196496 citations

Investigations on finite ideal quantum gases

H.-J. Schmidt, J. Schnack

arXiv:cond-mat/9803151Physica A Statistical Mechanics and its ApplicationsNov 1, 199833 citations

Calorimetry of a Bose–Einstein-condensed photon gas

Tobias Damm, Julian Schmitt, Qi Liang +4 more

Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases. Here we examine the thermodynamic behaviour of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of a nearly ideal Bose gas from the classical high temperature to the Bose-condensed quantum regime. The critical behaviour at the phase transition is clearly revealed by a cusp singularity of the specific heat. Regarded as a test of quantum statistical mechanics, our results demonstrate a quantitative agreement with its predictions at the microscopic level.Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases. Here we examine the thermodynamic behaviour of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of a nearly ideal Bose gas from the classical high temperature to the Bose-condensed quantum regime. The critical behaviour at the phase transition is clearly revealed by a cusp singularity of the specific heat. Regarded as a test of quantum statistical mechanics, our results demonstrate a quantitative agreement with its predictions at the microscopic level.

arXiv:1604.08747Nature CommunicationsApr 19, 201638 citations

Thermal properties of quantum gases

Luciano Colombo

Institute of Physics eBooksNov 1, 20220 citations

Ideal Quantum Gases

Franz Schwabl

Advanced texts in physicsJan 1, 20021 citation

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

is seen to be a special case. In the extreme relativistic region, the analogous special case is

n=1