Covariant Vortex In Superconducting-Superfluid-Normal Fluid Mixtures with Stiff Equation of State

TL;DR

This paper develops a covariant framework for analyzing vortices in mixtures of superconductors, superfluids, and normal fluids using a stiff relativistic equation of state, with applications to various physical systems.

Contribution

It introduces a covariant method to compute integrals of motion for vortices in fluid mixtures with a stiff equation of state, extending to multiple physical systems.

Findings

Derived integrals of motion for vortices in relativistic fluid mixtures.

Applied the framework to models including superfluid neutron stars and superconductors.

Abstract

The integrals of motion for a cylindrically symmetric stationary vortex are obtained in a covariant description of a mixture of interacting superconductors, superfluids and normal fluids. The relevant integrated stress-energy coefficients for the vortex with respect to a vortex-free reference state are calculated in the approximation of a ``stiff'', i.e. least compressible, relativistic equation of state for the fluid mixture. As an illustration of the foregoing general results, we discuss their application to some of the well known examples of ``real'' superfluid and superconducting systems that are contained as special cases. These include Landau's two-fluid model, uncharged binary superfluid mixtures, rotating conventional superconductors and the superfluid neutron-proton-electron plasma in the outer core of neutron stars.