Stability criterion for superfluidity based on the density spectral function

We study a stability criterion hypothesis for superfluids expressed in terms of the local density spectral function I_n(r,ω) that is applicable to both homogeneous and inhomogeneous systems. We evaluate the local density spectral function in the presence of a one-dimensional repulsive or attractive external potential within Bogoliubov theory, using solutions for the tunneling problem. We also evaluate the local density spectral function using an orthogonal basis, and calculate the autocorrelation function C _n(r,t). When superfluids in a d-dimensional system flow below a threshold, I_n(r,ω)â̂ωd holds in the low-energy regime and C_n(r,t)â̂1/td⁺1 holds in the long-time regime. However, when superfluids flow with the critical current, I_n(r,ω)â̂ωβ holds in the low-energy regime and C_n(r,t)â̂1/tβ⁺1 holds in the long-time regime with β<d. These results support the stability criterion hypothesis recently proposed.