Contribution to quantum statistical mechanics of cold gases

This thesis presents several results in statistical mechanics of cold gases. The first part mainly concerns non degenerate gases of fermions or bosons with spin (or pseudo-spin) 1/2. We derive a kinetic equation for such gases and use it to study spin transport properties, especially spin waves and Castaing's instability in a trap. Utilizing a hydrodynamic approach, we also calculate collective modes of oscillation of a one-dimensional trapped Bose gas at zero temperature. In a second part, we study equilibrium properties of dense cold gases. In the formalism of Ursell operators, we extend the quantum theory of cluster expansion from dilute to dense systems. This method is then used to study the statistics of exchange cycles in a Bose-Einstein condensate and the superfluid transition of an attractive Fermi gas. (author)