# Mutual Interactions of Phonons, Rotons, and Gravity

## TL;DR

This paper develops an effective point-particle framework to describe phonons, rotons, and their gravitational interactions in superfluids, unifying microscopic excitations and macroscopic objects within a single formalism.

## Contribution

It introduces a novel effective action formalism for particles in superfluids, capturing their interactions, decay processes, and gravitational couplings, extending previous models.

## Key findings

- Reproduces phonon decay and scattering predictions.
- Corrects classical roton-phonon scattering results.
- Shows phonons float and rotons sink in gravity with unique trajectories.

## Abstract

We introduce an effective point-particle action for generic particles living in a zero-temperature superfluid. This action describes the motion of the particles in the medium at equilibrium as well as their couplings to sound waves and generic fluid flows. While we place the emphasis on elementary excitations such as phonons and rotons, our formalism applies also to macroscopic objects such as vortex rings and rigid bodies interacting with long-wavelength fluid modes. Within our approach, we reproduce phonon decay and phonon-phonon scattering as predicted using a purely field-theoretic description of phonons. We also correct classic results by Landau and Khalatnikov on roton-phonon scattering. Finally, we discuss how phonons and rotons couple to gravity, and show that the former tend to float while the latter tend to sink but with rather peculiar trajectories. Our formalism can be easily extended to include (general) relativistic effects and couplings to additional matter fields. As such, it can be relevant in contexts as diverse as neutron star physics and light dark matter detection.