Josephson relation for disordered superfluids

Abstract

The Josephson sum rule relates the superfluid density to the condensate order parameter via the infrared residue of the single-particle Green's function. We establish an effective Josephson relation for disordered condensates valid upon ensemble averaging. This relation has the merit of showing explicitly how superfluidity links to the coherent density, i.e., the density of condensed particles with zero momentum. Detailed agreement is reached with perturbation theory for weak disorder.