Stability studies of first order spin-hydrodynamic frameworks

TL;DR

This paper investigates the stability of first-order spin-hydrodynamic models, revealing instabilities in certain modes and proposing the Frenkel condition as a stabilizing solution, despite some physical drawbacks.

Contribution

It compares two first-order spin-hydrodynamic frameworks with different assumptions about the spin chemical potential's order, analyzing their stability and proposing the Frenkel condition to eliminate instabilities.

Findings

Some spin modes are unstable at the linear perturbation level.

The Frenkel condition can remove instabilities in both frameworks.

Applying the Frenkel condition introduces physical drawbacks in one framework.

Abstract

We study the stability of first-order dissipative spin-hydrodynamic frameworks. We considered two different first-order dissipative spin-hydrodynamic frameworks. The first one considers the spin chemical potential ($\omega^{\alpha\beta}$) to be first order ($\mathcal{O}(\partial)$) in the hydrodynamic gradient expansion. The hydrodynamic gradient ordering of the spin chemical potential is a debatable issue within the frameworks of spin hydrodynamics. Therefore as a second choice, we also consider the spin hydrodynamic equations with $\omega^{\alpha\beta}\sim\mathcal{O}(1)$. We find that for both frameworks, at the level of linear perturbations some spin modes can be unstable. To remove these generic instabilities we consider the Frenkel condition. We argue that Frenkel condition helps get rid of the unstable solutions in both cases, but with a physical drawback for the case where $\omega^{\mu\nu}\sim\mathcal{O}(\partial)$.