The Study Of Thermodynamic Properties Of A Confined Fermi Gas With Weak Interaction

The investigation of ultracold degenerate Fermi gas is a new hot issue in current physics research. The experimental and theoretical researches of ultracold degenerate Fermi gases continue to advance at a dramatic pace. We believe that many novel physical discover will exhibit in front of us. With the development tendency: On one hand: Combining with ultracold degenerate Fermi gas and quantum control method of magnetic field Feshbach resonance, optical association and optical lattices, we could further research quantum and superfluidity phenomena of ultracold degenerate Fermi gas. On the other hand: Combining with ultracold degenerate Fermi gas and atom physics, condensed matter physics and optical physics, we will study the strongly connected problem of solid state physics and nuclear physics that wasn't solved finally.Ultracold degenerate Fermi gas has been applied abroadly in the manufacture of new material and new apparatus, duing to its particular characteristic, so the prospect is extremely broad.We discuss thermodynamical parameter of Fermi gas in a harmonic traps by using the the sum method for the grand canonical ensemble. Then we solve the energy eigenvalues of weakly interacting Fermi gas in a harmonic traps by using the simplest mean field theory-Hartree-Fock theory and the separation of variables. So that we can study the themodynamic properties of weakly interacting Fermi gas.The work of ours' can be divided into three parts:In the first part, we introduce the theoretical basis of studying Fermi gas: Fermi-Dirac statistics and thermodynamical parameter of Fermi gas. The statistics expression of thermodynamical parameter is different in variant limit and dimension.In the second part, we study the themodynamic properties of mesoscopic Fermi gas.Then discuss change of chemical potential and specific heat in the themodynamic limit and finite atom numbers.In the thrid part, We research thermodynamical properties of weakly interacting Fermi gas in a harmonic traps by using the mean field theory , then compare with mesoscopic Fermi gas.