Local Equilibrium Spin Distribution From Detailed Balance

TL;DR

This paper derives the local equilibrium spin distribution function from detailed balance in fermionic systems, showing how spin polarization can be generated from thermal vorticity in a quark model.

Contribution

It introduces a derivation of the local equilibrium spin distribution based on detailed balance, applying kinetic theory to the NJL model with semi-classical and non-perturbative expansions.

Findings

Non-zero spin polarization can be generated from an initially unpolarized system.

Spin polarization arises from thermal vorticity and is orthogonal to particle momentum.

The derivation connects spin polarization to fundamental kinetic and thermodynamic principles.

Abstract

As the core ingredient for spin polarization, the local equilibrium spin distribution function is derived from the detailed balance principle. The kinetic theory for interacting fermionic systems is applied to the Nambu--Jona-Lasinio model at quark level. Under the semi-classical expansion with respect to $\hbar$ and non-perturbative expansion with respect to $N_c$, the kinetic equations for the vector and axial-vector distribution functions are derived with collision terms. It is found that, for an initially unpolarized system, non-zero spin polarization can be generated at the order of $\hbar$ from the coupling between the vector and axial-vector charges. The local equilibrium spin polarization is derived from the requirement of detailed balance. It arises from the thermal vorticity and is orthogonal to the particle momentum.