Derivation of hydrodynamics for the gapless mode in the BEC-BCS   crossover from the exact one-loop effective action
  We show that many hydrodynamical properties of the BEC/BCS crossover in the presence of a Feshbach resonance at T=0 can be derived easily from the derivative expansion of the (exact) fully renormalized one-loop effective action. In particular, we calculate the velocity of sound throughout the BCS and BEC regimes and derive the generalized superfluid continuity equations for the composite two-fluid system. 
Da-Shin Lee, Chi-Yong Lin and Ray J. Rivers