Kinetic approach to polarization-vorticity coupling and hydrodynamics with spin

TL;DR

This paper explores the relationship between spin polarization and vorticity using a kinetic approach, clarifying that thermal-vorticity and spin polarization tensors are not inherently equal, and proposes a hydrodynamic framework for spin-1/2 particles.

Contribution

It introduces a kinetic framework for spin-1/2 particles that distinguishes between thermal-vorticity and spin polarization, and outlines a hydrodynamic formulation based on semiclassical expansion.

Findings

Thermal-vorticity and spin polarization tensors are not necessarily equal.

A kinetic approach for spin-1/2 particles is developed.

A hydrodynamic framework for particles with spin is proposed.

Abstract

Recently introduced equilibrium Wigner functions for spin-one-half particles are used in the semiclassical kinetic equations to study the relation between spin polarization and vorticity. It is found, in particular, that such a framework does not necessarily imply that the thermal-vorticity and spin polarization tensors are equal. Subsequently, a procedure to formulate the hydrodynamic framework for particles with spin-one-half, based on the semiclassical expansion, is outlined.