Energy fluctuation and discontinuity of specific heat

TL;DR

This paper investigates the quantum-classical crossover of the relationship between energy fluctuation and specific heat in ideal Bose and Fermi gases, revealing a hump near the condensation point and discussing potential phase transition signatures.

Contribution

It analytically explores the deviation from classical energy fluctuation-specific heat relation in quantum gases and identifies a characteristic hump indicating possible phase transition behavior.

Findings

Hump in energy fluctuation ratio near Bose-Einstein condensation

Deviation from classical relation in quantum degenerate regime

Discussion of phase transition indicators in quantum gases

Abstract

Specific heat per particle ($c_v$) of an ideal gas, in many occasions, is interpreted as energy fluctuation per particle ($\triangle\epsilon^2$) of the ideal gas through the relation: $\triangle\epsilon^2=kT^2c_v$, where $k$ is the Boltzmann constant and $T$ is the temperature. This relationship is true only in the classical limit, and deviates significantly in the quantum degenerate regime. We have analytically explored quantum to classical crossover of this relationship, in particular, for 3-D free Bose and Fermi gases. We also have explored the same for harmonically trapped cases. We have obtained a hump of $\triangle\epsilon^2/kT^2c_v^{(\text{cl})}$ around the condensation point for 3-D harmonically trapped Bose gas. We have discussed the possibility of occurring phase transition with discontinuity of heat capacity from existence of such a hump for other Bose and Fermi systems.