  Recent experiments on disordered superconductors find that the superfluid
density $n_s(T)$ decreases dramatically and characteristically with disorder,
differently from what is expected for a mean order parameter field or BCS,
amplitude only, picture for the superconductor. We describe here a new
microscopic free energy functional which explicitly describes its dependence on
both the amplitude and phase of superconducting order, in a gauge invariant
manner. We use this here in an approximation of noninteracting phase
fluctuations (Gaussian or harmonic approximation) to obtain $n_s(T)$ in the
presence of (static) disorder. We compare our results successfully with
experiment.
