Josephson relation for disordered superfluids

TL;DR

This paper derives an effective Josephson relation for disordered superfluids, linking superfluid density to the coherent density, and confirms its validity through perturbation theory for weak disorder.

Contribution

It introduces a new Josephson relation applicable to disordered condensates, extending the understanding of superfluidity in disordered systems.

Findings

Agreement with perturbation theory for weak disorder

Explicit connection between superfluidity and coherent density

Effective relation valid upon ensemble averaging

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 to show explicitly how superfluidity links to the coherent density, i.e., the density of particles with zero momentum. Detailed agreement is reached with perturbation theory for weak disorder.