Transport theory for cold relativistic superfluids from an analogue model of gravity

TL;DR

This paper develops a covariant transport theory for phonons in relativistic superfluids using a gravity analogue model, providing insights into transport phenomena relevant to high-density QCD phases in neutron stars.

Contribution

It introduces a relativistic kinetic theory for superfluid phonons based on a gravity analogy, extending previous models to a covariant framework applicable at small temperatures.

Findings

Derived covariant hydrodynamical equations for phonons.

Constructed a kinetic theory using a gravity analogue model.

Applied the framework to the color-flavor locked phase in neutron stars.

Abstract

We write a covariant transport equation for the phonon excitations of a relativistic superfluid valid at small temperatures. The hydrodynamical equations for this system are derived from the effective field theory associated to the superfluid phonons. We describe how to construct the kinetic theory for the phonon quasiparticles using a relativistic generalization of the analogue model of gravity developed by Unruh. This gravity analogy relies on the equivalence between the action of a phonon field moving in a superfluid background with that of a boson propagating in a given curved space-time. Exploiting this analogy we obtain continuity equations for the phonon current, entropy and energy-momentum tensor in a covariant form, valid in any reference frame. Our aim is to shed light on some aspects of transport phenomena of relativistic superfluidity. In particular, we are interested in the low temperature regime of the color flavor locked phase, which is a color superconducting and superfluid phase of high density QCD that may be realized in the core of neutron stars.