Side-Jump Induced Spin-Orbit Interaction of Chiral Fluids from Kinetic Theory

TL;DR

This paper uses kinetic theory to explore how quantum corrections induce spin-orbit interactions in chiral fluids, affecting angular momentum conservation and polarization under various conditions.

Contribution

It introduces a detailed kinetic theory analysis of spin-orbit interactions in chiral fluids, highlighting the role of quantum corrections and local equilibrium effects.

Findings

Quantum corrections lead to nonzero anti-symmetric energy-momentum tensor components.

In global equilibrium, angular momentum conservation involves cancellation between orbital and spin parts.

Near local equilibrium, angular momentum is not conserved due to spin-orbit interactions and temperature/chemical potential gradients.

Abstract

We apply the Wigner-function approach and chiral kinetic theory to investigate the angular momentum and polarization of chiral fluids composed of Weyl fermions with background electric/magnetic fields and vorticity. It is found that the quantum corrections in Wigner functions give rise to nonzero anti-symmetric components in the canonical energy-momentum tensors, which are responsible for the spin-orbit interaction. In global equilibrium, conservation of the canonical angular momentum reveals the cancellation between the orbital component stemming from side jumps with nonzero vorticity and the spin component in the presence of an axial chemical potential. We further analyze the conservation laws near local equilibrium. It turns out that the canonical angular momentum is no longer conserved even in the absence of background fields due to the presence of a local torque coming from the spin-orbit interaction involving temperature/chemical-potential gradients, which is implicitly led by collisions.