The unitary Fermi gas

This dissertation is concerned with the physics of dilute Fermi gases in a regime of short-range attractive interactions and large scattering lengths. This work represents the first non-perturbative determination of the thermal properties of these gases at and around the so-called unitary regime (infinite scattering length). The behavior of these gases is universal: they describe systems of cold atoms as well as dilute neutron matter. The properties computed here include energy, entropy, chemical potential, condensate fraction, critical temperature for superfluidity and quasiparticle spectrum. The calculation of some of these properties for atomic gases in traps is also presented and compared with experimental data, with which remarkable agreement is found. In addition, the results are presented here of a next-to-next-to-leading order epsilon expansion calculation of the ground state energy per particle of a unitary Fermi gas.