On the specific heat of a fermionic atomic cloud in the unitary regime

TL;DR

This paper investigates the complex temperature dependence of the specific heat in a fermionic atomic cloud at unitarity, highlighting different regimes dominated by collective modes and surface effects.

Contribution

It provides a detailed analysis of the specific heat's temperature dependence across various regimes in a unitary fermionic cloud, emphasizing the role of collective and surface modes.

Findings

Specific heat exhibits exponential, linear, and quartic temperature dependencies.

Different temperature regimes are dominated by distinct collective modes.

Intermediate temperatures show a gradual change in the power-law behavior.

Abstract

In the unitary regime, when the scattering amplitude greatly exceeds in magnitude the average inter-particle separation, and below the critical temperature thermal properties of an atomic fermionic cloud are governed by the collective modes, specifically the Bogoliubov-Anderson sound modes. The specific heat of an atomic cloud in a elongated trap in particular has a rather compex temperature dependence, which changes from an exponential behavior at very low temperatures ($T\ll\hbar\omega_{||}$), to $\propto T$ for $\hbar\omega_{||}\ll T \ll \hbar\omega_\perp$ and then continuosly to $\propto T^4$ at temperatures just below the critical temperature, when the surface modes play a dominant role. Only the low ($\hbar\omega_{||} \ll T \ll \hbar\omega_\perp$) and high ($\hbar\omega_\perp \ll T < T_c$) temperature power laws are well defined. For the intermediate temperatures one can introduce at most a gradually increasing with temperature exponent.