| Quantum degenerate Fermi gases can be created in the laboratories using alkali atoms. These gases can be in different regimes of density and interaction strength and provide an ideal test bed for the basic properties of the quantum and statistical mechanics. Also some astrophysical objects such as neutron stars can be idealized as interacting fermion systems. In this thesis work, the ground state properties of dilute Fermi gases with attractive short range two-body interactions are reported. Main results of this work are produced by application of quantum Monte Carlo methods. We introduce variational nodal structure to the trial wave function in order to deal with the fermion sign problem. We consider the possibility of Cooper pairing between fermions of different species. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the s-wave scattering length a and the Fermi wave vector k F. We also review some of the conventional variational methods such as the Lowest Order Constrained Variational which is suitable for Fermi fluids without pairing correlation. The ground state energy, pairing gap Delta, quasi-particle spectrum, two-body distribution function, and momentum distribution of the superfluid were studied with greater accuracy using ab initio quantum Monte Carlo techniques.; In the case of the two component Fermi fluid, we find that in the weak coupling regime, 1/akF < -1, the system is a Bardeen-Cooper-Schrieffer type superfluid and the energy gap Delta is much smaller than the Fermi gas energy EFG. For 1/akF ≥ 0.5 we find that weakly interacting composite bosons or molecules are formed in the superfluid gas with Delta and gas energy per particle approaching half of the molecular energy |Emol|/2. In this region we seem to have Bose-Einstein condensation of molecules. The behavior of the energy, chemical potential and energy gap in the transition region, -0.5 < 1/ak F < 0.5, is discussed.; The study is extended to the three component Fermi fluid in relation to the spin polarized alkali gases and color superconductivity of the quark matter. |
