Superfluid two-stream instability in a microscopic model

The superflow in a superfluid is bounded from above by Landau's critical velocity. Within a microscopic bosonic model, I show that below this critical velocity there is a dynamical instability that manifests itself in an imaginary sound velocity and that is reminiscent of the two-stream instability in electromagnetic plasmas. I compute the onset of this instability and its full angular structure in a relativistic, uniform superfluid for all temperatures. At weak coupling, the instability only operates in a very small region in the phase diagram of temperature and superflow. Varying the coupling of the model suggests that the effect is more prominent at strong coupling and thus could be important for superfluids in compact stars and in the laboratory.