Generalized Criterion for Stability of Superflow Past an Obstacle

Abstract

We propose a new criterion of stability or instability of one-directional superflow of Bose condensates. In d-dimensional condensates with steady superflow, spectral function $\rho(\mathbf {r},\omega)=\sum_{l}|\langle l|\hat{n}(\mathbf{r})|\mathrm{g}\rangle|^{2}\delta (\omega-E_{l}+E_{\mathrm{g}})$ of the local density $\hat{n}(\mathbf{r})$ at the critical velocity behaves as ρ(r,ω)∝ ω ^β with β<d at low ω while ρ(r,ω)∝ ω ^d below the critical velocity. We confirm the validity of our criterion within the Gross-Pitaevskii-Bogoliubov theory. In the presence of a penetrable repulsive potential, β is given by d−2 at the critical velocity, where gray-soliton-phonon emission leads to the breakdown of superfluidity. In the case of the Landau instability in spatially uniform systems, on the other hand, β=−1/3,1/3,1 for d=1,2,3, respectively.