By Landau's theory the normal mass density(total density minus the superfluid mass density) is the total mass carried by excitations. For the BCS state and weakly interacting Bose gas the normal density is zero at zero temperature because there are no excitations. However in the presence of disorder, the normal density is not zero even at zero temperature. My question is: Is there a general argument (conservation law or symmetry consideration) by which one can determine whether the normal density is nonzero at zero temperature? Or genereally for what kind of system the superfluid density is not the total density at zero temperture?