2013/05/31 by Shohei Watabe, Yusuke Kato
Mathematics · Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Condensed matter physics #Energy (signal processing) #Function (biology) #Mathematical physics #Mathematics #Omega #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Spectral function #Superfluidity #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.88.063612
published as Phys. Rev. A 88, 063612 (2013) · 18 pages, 10 figures
arxiv created 2013/12/04 · openalex publication_date 2013/12/06 · arxiv updated 2013/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a stability criterion hypothesis for superfluids expressed in terms of the local density spectral function In(r,\ensuremathω) 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 Cn(r,t). When superfluids in a d-dimensional system flow below a threshold, In(r,\ensuremathω)\ensuremath∝\ensuremathωd holds in the low-energy regime and Cn(r,t)\ensuremath∝1/td+1 holds in the long-time regime. However, when superfluids flow with the critical current, In(r,\ensuremathω)\ensuremath∝\ensuremathω^\ensuremathβ holds in the low-energy regime and Cn(r,t)\ensuremath∝1/t^\ensuremathβ+1 holds in the long-time regime with \ensuremathβ<d. These results support the stability criterion hypothesis recently proposed.