| The topic of this thesis is to understand the behavior of a two component Fermi gas close to a diverging s-wave scattering length. These systems are realized in cold atom physics, where the two fermionic species are trapped in two different Zeeman states. Then, the gas is magnetically brought close to a resonance, which corresponds to a different scattering channel, where the electronic spin of the colliding particles is temporarily rearranged.; Because of the low temperatures, the atoms in each Zeeman state are in a deep quantum degenerate state and this is the realm of Fermi liquid theory.; Being the system close to a resonant state, implies that strong many body fluctuations occur. Despite this, the theories of these gases, at this time, mostly consider the Random Phase approximation. A perturbative theory, though, is not sufficient close to a resonance, since the scattering length goes to infinity and therefore their solution can give only qualitative answers.; In this thesis, I show that, in particular, the exchange fluctuations, close to the resonance, are fundamental if we want to understand the physics of the system. It is, in fact, due to these effects that the scattering length gets renormalized correctly, giving a finite value, as it is observed experimentally, whereas the RPA description fails, as we show, since it diverges even before the resonance is reached.; Whether the system is a Fermi liquid on both sides of the resonance is still an open question, which I believe, I answer in this thesis, by providing a full account of its thermodynamics, that can be tested experimentally. Through the theory we present, in which we readapt the method of Babu and Brown, we are able to calculate from the microscopic Hamiltonian, the Landau parameters which enter the thermodynamics properties of the system, close to resonance, together with some dynamical properties also for spin polarized systems. We focus our attention to the normal phase, since this is the only way a Fermi liquid theory can be tested. |
