Bogoliubov Theory for a Superfluid Bose Gas Flowing in a Random Potential: Stability and Critical Velocity

We investigate the stability and critical velocity of a weakly interacting Bose gas flowing in a random potential. By applying the Bogoliubov theory to a disordered Bose system with a steady flow, the condensate density and the superfluid density are determined as functions of the disorder strength, flow velocity, and temperature. The critical velocity, at which the steady flow becomes unstable, is calculated from the spectrum of hydrodynamic excitation. We also show that in two dimensions the critical velocity strongly depends on the system size.