Fluctuation Spectral Functions and Phase Transitions for Cold Fermi Gases in 2D

We study cold fermions in 2D that are interacting through the s-wave contact potential, using the path-integral formalism. The phase transitions are investigated using the joint solution of the gap and number equations. In the latter ones, the amplitude and phase fluctuations are taken into account within the t-matrix NSR-type formalism. It is shown that convergent solutions for the fermion density in 2D can be obtained even in the lowest-order (quadratic) approximation for fluctuations with a proper determination of the spectral functions. This approach leads, in particular, to a non-coherent quasicondensate which exists between the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature below which the system is superfluid and a transition temperature T (Delta) above which the quasicondensate is destroyed.