Thermodynamics Of Fermi Gas At Unitary Regime

An impressive amount of experimental achievements has characterized the past ten years of ultracold Fermi gas physics.In these experiments a crucial tool is the application of the Feshbach resonences.With Feshbach resonences the scattering lengths between atoms can be altered,particularly,in the so-called unitary regime,the scattering lengths diverge,which results a universal behaviour.Because similar universal properties appear in other strongly interacting Fermi systems,unitary Fermi gas provides a new way to explore the strongly interacting systems.However,due to a lack of small interacting parameters,the standard perturbation theory is invalid.The mean-field theory can give a qualitative description though,the results have a clear deviation from the experiments.Based on the universality hypothesis,we attempt an analysis of those experiments from a viewpoint of macroscopic equilibrium state.At high temperature,the fugacity of the system z=exp(μ/kBT)<<1,which allows a semi-classical virial expansion.In this thesis two results are obtained:1.First,we obtain the density of unitary Fermi gas in a trap using dynamical equilibrium conditions and Gibbs-Duhem relation.Then the relevant thermal quantities are calculated. An estimate of universal parameter P=-0.97is also given.2.Based on the virial expansions we express the thermal quantities of unitary Fermi gas as the functions of density and temperature only,which confirms the universal behaviour at high temperature.