Spin Boltzmann equation for non-relativistic spin-1/2 fermions

TL;DR

This paper derives the spin Boltzmann equations for non-relativistic spin-1/2 fermions with contact interactions, providing a clear formulation of spin coupling in collisions and exploring equilibrium and off-shell effects.

Contribution

It introduces a compact form of the spin collision terms and derives the on-shell spin Boltzmann equation up to next-to-leading order, including spin chemical potential emergence.

Findings

Explicit form of spin matrix elements in collision terms

Derivation of equilibrium spin distribution from collision term

Discussion of off-shell contributions to the spin Boltzmann equation

Abstract

We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in collision terms can be completely worked out and be put into such a compact form that one can clearly see how spins are coupled in particle scatterings. A semi-classical expansion in the Planck constant has been made and the on-shell part of the spin Boltzmann equation up to the next-to-leading order is derived. At the leading order the equilibrium spin distribution can be obtained from the vanishing of the collision term for the spin density. The spin chemical potential emerges as a natural consequence of spin conservation. The off-shell part of the spin Boltzmann equation is also discussed. The work can be extended to more sophisticated interaction such as nuclear force in order to apply to spin polarization phenomena in heavy-ion collisions at low energies.