  We investigate the physics of an adiabatic transition from a BCS
superconductor to a Fermi liquid for an exponentially slow decreasing pairing
interaction. In particular, we show that the metal keeps memory of the parent
BCS state so it is possible to reverse the dynamics and go back to the original
state similarly to a spin/photon echo experiment. Moreover, we study the
evolution of the order parameter phase phi in transforming the BCS
superconductor to a conventional metal. Since the global phase is the conjugate
variable of the density we explicitly show how to use the dynamics of phi
together with gauge invariance to build up the non-interacting chemical
potential away from particle-hole symmetry. We further analyze the role of phi
in restoring the gauge invariant current response when the non-interacting
Fermi liquid is approached starting from a BCS superconductor in the presence
of an external vector field.
