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We investigate the physics of an adiabatic transition from a BCSsuperconductor to a Fermi liquid for an exponentially slow decreasing pairinginteraction. In particular, we show that the metal keeps memory of the parentBCS state so it is possible to reverse the dynamics and go back to the originalstate similarly to a spin/photon echo experiment. Moreover, we study theevolution of the order parameter phase phi in transforming the BCSsuperconductor to a conventional metal. Since the global phase is the conjugatevariable of the density we explicitly show how to use the dynamics of phitogether with gauge invariance to build up the non-interacting chemicalpotential away from particle-hole symmetry. We further analyze the role of phiin restoring the gauge invariant current response when the non-interactingFermi liquid is approached starting from a BCS superconductor in the presenceof an external vector field.

Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics