Study Of The Isothermal Compressibility Of Unitary Fermi Gas

The study of strongly unitary Fermi gas thermodynamics is a hot topic, due to the rapid development of the Feshbach resonance technique. It belongs to the study of quantum many-body theory.This paper first reviews the basic knowledge and theory that deal with the interaction of quantum Fermi gases. We review the basic of s-scattering theory, the Feshbach resonance experiment, polarized tensor operator and the finite temperature integration of Matsubara function of boson-fermium mixture system.The thermodynamic characteristics of the strongly interacting unitary fermium system can exhibit the thermodynamic universality. The thermodynamic laws of the strongly interacting unitary Fermi gas are similar to those of non-interacting ideal gas. For example, the Virial theorem between pressure and energy density of the ideal gas is still satisfied with unitary Fermi gas. In the literature the sound velocity of unitary Fermi gas has been analyzed. The expression of sound velocity formula of unitary Fermi gas is identical to that of the ideal quantum gas, as well as the ideal classical gas. Based on the knowledge of thermodynamics, sound velocity and the isothermal compressibility are closely related. The isothermal compressibility of strongly interacting Fermi is the main goal of our research. We should answer the question that the isothermal compressibility of strongly interacting Fermi is similar to that of the ideal quantum or classical gas.In this paper, the isothermal compressibility of the unitary Fermi gas is analyzed. The theoretical analysis and numerical results show that the isothermal compression coefficient formula is not universal. The isothermal compression coefficient expression of unitary Fermi gas can reflect the dynamic detail better than the sound velocity.