From Field Theory to the Hydrodynamics of Relativistic Superfluids

TL;DR

This paper derives the hydrodynamics of relativistic superfluids from microscopic quantum field theory, providing analytic and numerical results for superfluid properties, sound velocities, and superflow effects across temperature regimes.

Contribution

It introduces a field-theoretic approach to relativistic superfluid hydrodynamics, including analytic calculations and the application of the 2PI formalism for all temperatures.

Findings

First and second sound velocities depend on temperature and superflow.

Role reversal of density and temperature waves occurs at high temperatures.

Application to dense quark and nuclear matter in stars.

Abstract

The hydrodynamic description of a superfluid is usually based on a two-fluid picture. In this thesis, basic properties of such a relativistic two-fluid system are derived from the underlying microscopic physics of a complex scalar quantum field theory. To obtain analytic results of all non-dissipative hydrodynamic quantities in terms of field theoretic variables, calculations are first carried out in a low-temperature and weak-coupling approximation. In a second step, the 2-particle-irreducible formalism is applied: This formalism allows for a numerical evaluation of the hydrodynamic parameters for all temperatures below the critical temperature. In addition, a system of two coupled superfluids is studied. As an application, the velocities of first and second sound in the presence of a superflow are calculated. The results show that first (second) sound evolves from a density (temperature) wave at low temperatures to a temperature (density) wave at high temperatures. This role reversal is investigated for ultra-relativistic and near-nonrelativistic systems for zero and nonzero superflow. The studies carried out in this thesis are of a very general nature as one does not have to specify the system for which the microscopic field theory is an effective description. As a particular example, superfluidity in dense quark and nuclear matter in compact stars are discussed.