Dynamics of a relative superflow between a Bose-Einstein condensate and the thermal cloud

We use the classical fields approximation to study a translational flow of the condensate with respect to the thermal cloud in a weakly interacting Bose gas confined in a three-dimensional box. We study both subcritical and supercritical relative velocity cases and analyze in detail a state of stationary flow which is reached in the dynamics. This state corresponds to the thermal equilibrium, which is characterized by the relative velocity of the condensate and the thermal cloud. We observe two processes-re-thermalization and drag, both of which lead to a reduction of a relative velocity of the superflow. Yet only the drag process, which is observed above the critical velocity v(cr), results in transferring a Bose-Einstein condensate to a slower moving mode. In this case the relative velocity of the flow suddenly drops to a value close to zero. Finally, we report the critical velocity to be for our parameters v(cr)=0.21c for the initial condition and v(cr)(eq)=0.12c for re-thermalized superflow (c being the Landau speed of sound), which is strikingly lower than Landau critical velocity, yet consistent with experiments.