Generalized criterion for stability of superflow past an obstacle

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(r,ω=∑ _l|〈l|n̂ (r)| g〉| ² δ (ω-E _l+E _g) of the local density n̂(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.