From a complex scalar field to the two-fluid picture of superfluidity

The hydrodynamic description of a superfluid is usually based on a two-fluid picture. We compute the basic properties of the relativistic two-fluid system from the underlying microscopic physics of a relativistic \varphi^4 complex scalar field theory. We work at nonzero but small temperature and weak coupling, and we neglect dissipation. We clarify the relationship between different formulations of the two-fluid model, and how they are parameterized in terms of partly redundant current and momentum 4-vectors. As an application, we compute the velocities of first and second sound at small temperatures and in the presence of a superflow. While our results are of a very general nature, we also comment on their interpretation as a step towards the hydrodynamics of the color-flavor locked state of quark matter, which, in particular in the presence of kaon condensation, appears to be a complicated multi-component fluid.