Non-equilibrium effective field theory and second sound

TL;DR

This paper explores second sound phenomena across different states of matter using non-equilibrium effective field theories, revealing multiple EFTs with and without second sound and proposing new formulations to unify these descriptions.

Contribution

It introduces a novel framework for constructing multiple EFTs for second sound in matter, utilizing coset methods and new manifold formulations to unify different descriptions.

Findings

Existence of multiple EFTs for second sound at finite temperature.

Identification of inverse Higgs constraints as key to differences between EFTs.

Proposal of a new manifold approach to unify EFT descriptions.

Abstract

We investigate the phenomenon of second sound in various states of matter from the perspective of non-equilibrium effective field theory (EFT). In particular, for each state of matter considered, we find that at least two (though sometimes multiple) qualitatively different EFTs exist at finite temperature such that there is always at least one EFT with a propagating second-sound wave and at least one with no such second-sound wave. To aid in the construction of these EFTs, we use the method of cosets developed for non-equilibrium systems. It turns out that the difference between the EFTs with and without second-sound modes can be understood as arising from different choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that it is possible to bypass the need for new inverse Higgs constraints by formulating EFTs on a new kind of manifold that is like the usual fluid worldvolume, but with reduced gauge symmetries.