Spin waves in spin hydrodynamics

TL;DR

This paper investigates the propagation of spin waves within relativistic hydrodynamics, deriving their velocity, polarization characteristics, and damping effects, revealing that only transverse spin degrees propagate and their speed approaches half the speed of light.

Contribution

It provides an analytical expression for spin wave velocity in relativistic fluids and explores the effects of dissipation and particle statistics on spin wave damping.

Findings

Spin wave velocity approaches half the speed of light in ultra-relativistic limit.

Only transverse spin degrees propagate as waves.

Damping coefficients depend on particle statistics and dissipative effects.

Abstract

The propagation properties of spin degrees of freedom are analyzed in the framework of relativistic hydrodynamics with spin based on the de Groot--van Leeuwen--van Weert definitions of the energy-momentum and spin tensors. We derive the analytical expression for the spin wave velocity for arbitrary statistics and show that it goes to half the speed of light in the ultra-relativistic limit. We find that only the transverse degrees of freedom propagate, analogously to electromagnetic waves. Finally, we consider the effect of dissipative corrections and calculate the damping coefficients for the case of Maxwell-J\"uttner statistics.