Massless fermions in null Fermi coordinates and an application to analog gravity in $\text{He}^3$-A

TL;DR

This paper investigates how massless quasiparticles in superfluid helium-3 experience effective curvature and magnetic interactions, using null Fermi coordinates to analyze their spin coupling in analog gravity scenarios.

Contribution

It introduces a null Fermi coordinate framework to study spin-curvature coupling of massless quasiparticles in superfluid helium-3- A, providing new insights into analog gravity effects.

Findings

Derived an effective magnetic interaction due to curvature coupling.

Set up null Fermi coordinates for radial and circular geodesics.

Provided numerical estimates of the curvature effects.

Abstract

Bogoliubov quasiparticles moving in the background of superfluid $\text{He}^3$-A see an apparently curved space-time metric when the background superfluid vacuum is in motion. We study how this curvature couples with the spins of the effectively massless quasiparticles. First, we set up the problem in null Fermi coordinates for radial as well as circular geodesics and then use it in the context of the analog metric seen by the quasiparticles. We obtain an effective magnetic interaction due to curvature coupling, and provide numerical estimates. Some possible implications of these results are then pointed out.