Hydrodynamic Study Of The Collective Modes In The Unitary Fermi Gases

The study of nuclear many-body systems has attracted much attention. It is quite a challenging task especially when strong couplings are involved, due to the lack of both experimental controllability and small perturbative parameters. One reasonable scheme is to benefit from the exploration of other controllable systems, such as the unitary Fermi gases, which is our main subject.The unitary Fermi gas is a strongly interacting quantum Fermi gas. In a two-component Fermi gas, the interaction between different spin species can be tuned by an external mag-netic field. The s-wave scattering length diverges at certain magnetic field, while the cross section saturates the unitary limit. This phenomenon is called Feshbach resonance. The strongly interacting system obtained this way is called the unitary Fermi gas. The behav-ior of such gases is independent of the microscopic detail of the inter-particle interaction, showing universality. The unitary Fermi gas provides a good paradigm for strongly inter-acting systems in nature, since it can be easily produced and controlled in experiments. The study of the unitary Fermi gases may shed light on the properties of other physi-cal systems, including high temperature superconductor, neutron star, and quark-gluon plasma (QGP). An important motivation of this dissertation is to find some clue for the study of the QGP in the exploration of the unitary Fermi gases.In this dissertation, a new method was proposed to investigate the dynamic processes of the unitary Fermi gasses. Based on hydrodynamics, we established a set of differential equations to describe the dynamics of the unitary Fermi gases in a trapping potential. With proper initial conditions, the simultaneous equations can be numerically solved. The col-lective modes can thus be obtained. We studied the frequency and the temporal damping rate of the axial breathing mode. The dependence of the damping rate on the experimen- tal conditions has been analyzed, and a specific function is given. Comparison with the experiments gives an estimate of the shear viscosity, which is an important property in the study of both the unitary Fermi gases and the QGP. The scissors mode is also studied in the framework of hydrodynamics. We obtained the time evolution of the density and velocity distribution, as well as the frequency and the damping rate. Analysis shows that the damping rate is proportional to the shear viscosity. The damping rate at minimum viscosity is predicted by this means.We also investigated the bulk properties and the collective modes of a trapped Fermi gas near the unitary limit. The ground state energy of the gas with the scattering length near negative infinity is obtained, and the results are in good agreement with the Monte Carlo calculations. The frequencies of the axial and radial breathing modes in this region are also studied, showing good agreement with the experimental data.