Fermi Condensates In A Collective Effect

This Thesis cosists with two parts.The one is collective effects of Fermi condensates, the other is the Feynman diagram method for fermi condensate.In part one,a perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper -Schrieffer(BCS) superfluid to Bose-Einstein condensation(BEC).Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond mean-field approximation,the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation.Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS,BEC,and unitarity limits are provided explicitly and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.In part two,considering the field theory may fail in the correlation systems at the condensed state such as BCS and BCS-BEC crossover,we re-deduce the Fevnman diagram and relevant perturbation theory in the Fermi condensate,and find a diagram method with abnormal Green function as well as present a generalized perturbation theory with H=0+H.Then,based on the Boson-Fermion model, we give the partition flmction,the critical temperature,the fermion's chemical potential and the gap energy of the BCS-BEC crossover.We also propose a possible explanation for the pseudo-gap in high temperature superconductivity.