# Multicomponent meson superfluids in chiral perturbation theory

## TL;DR

This paper models multicomponent meson superfluids using chiral perturbation theory, analyzing two pion gases with different isospin chemical potentials and exploring the effects of symmetry locking on stability and excitations.

## Contribution

It derives the chiral Lagrangian for two pion gases and investigates the impact of symmetry locking on the system's spectrum and potential instabilities.

## Key findings

- Weak locking does not cause instability.
- Strong locking leads to tachyonic modes.
- Potential transition to inhomogeneous phase.

## Abstract

We show that the multicomponent meson systems can be described by chiral perturbation theory. We chiefly focus on a system of two pion gases at different isospin chemical potential, deriving the general expression of the chiral Lagrangian, the ground state properties and the spectrum of the low-energy excitations. We consider two different kinds of interactions between the two meson gases: one which does not lock the two chiral symmetry groups and one which does lock them. The former is a kind of interaction that has already been discussed in mutlicomponent superfluids. The latter is perhaps more interesting, because seems to be related to an instability. Although the pressure of the system does not show any instability, we find that for sufficiently strong locking, the spectrum of one Bogolyubov mode becomes tachyonic. This unstable branch seems to indicate a transition to an inhomogeneous phase.