Abstract
Fermi-surface bosonization is used to show that the long-wavelength, T=0, dynamics of a BCS superfluid or superconductor is described by a galilean invariant non-linear time-dependent Schrödinger equation. This equation is of same form as the Gross-Pitaevskii equation for a Bose superfluid, but the “wavefunction” is not the superfluid order parameter.
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