Stability Criterion for Superfluidity based on the Density Spectral Function

Abstract

We study a stability criterion hypothesis for superfluids in terms of the the local density spectral function $I_n(r,\omega )$ applicable both to homogeneous and inhomogeneous systems. We evaluate the local density spectral function in the presence of a one-dimensional repulsive/attractive external potential within the Bogoliubov theory using solutions of 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 flow below a threshold, we find that in the $d$-dimensional system, $I_n(r,\omega )\propto {\omega }^d$ in the low-energy regime and $C_n(r,t)\propto 1/t^{d+1}$ in the long-time regime hold. When superfluids flow with the critical current, on the other hand, we find $I_n(r,\omega )\propto {\omega }^{\beta }$ in the low-energy regime and $C_n(r,t)\propto 1/t^{\beta +1}$ in the long-time regime with $\beta <d$. These results support the stability criterion hypothesis recently proposed.

18 pages, 10 figures

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Cited by in corpus (4)

• Metastability, excitations, fluctuations, and multiple-swallowtail structures of a superfluid in a Bose-Einstein condensate in the presence of a uniformly moving defect
• Instability of the superfluid flow as black-hole lasing effect
• Current production in ring condensates with a weak link
• Nonequilibrium steady states of Bose-Einstein condensates with a local particle loss in double potential barriers