Damping of spin waves

TL;DR

This paper demonstrates that in ideal-spin hydrodynamics, spin tensor components obey damped wave equations with damping rates linked to particle collisions, affecting spin equilibration timescales in heavy-ion collisions.

Contribution

It introduces a semi-classical approach to quantify spin damping rates due to nonlocal collisions in spin-1/2 fermion systems, highlighting their potential non-equilibrium during heavy-ion freeze-out.

Findings

Spin components follow damped wave equations.

Relaxation times can be much longer than typical dissipative times.

Spin may not reach equilibrium by freeze-out in heavy-ion collisions.

Abstract

We show that, in ideal-spin hydrodynamics, the components of the spin tensor follow damped wave equations. The damping rate is related to nonlocal collisions of the particles in the fluid, which enter at first order in $\hbar$ in a semi-classical expansion. This rate provides an estimate for the timescale of spin equilibration and is computed by considering a system of spin-1/2 fermions interacting via a quartic self-interaction as well as via (screened) one-gluon exchange. It is found that the relaxation times of the components of the spin tensor can become very large compared to the usual dissipative timescales of the system. Our results suggest that the spin degrees of freedom in a heavy-ion collision may not be in equilibrium by the time of freeze-out, and thus should be treated dynamically.