Bose-representation for a strongly coupled nonequilibrim fermionic superfluid in a time-dependent trap

Using the functional integral formulation of a nonequilibrium quantum many-body theory we develop a regular description of a Fermi system with a strong attractive interaction in the presence of an external time-dependent potential. In the strong coupling limit this fermionic system is equivalent to a noequilibrium dilute Bose gas of diatomic molecules. We also consider a nonequilibrim strongly coupled Bardeen-Cooper-Schrieffer (BCS) theory and show that it reduces to the full nonlinear time-dependent Gross-Pitaevski (GP) equation, which determines an evolution of the condensate wave function.